Daniele Semola

Generating author description...

All published works

Action	Title	Year	Authors
+ PDF Chat	Fundamental groups and the Milnor conjecture	2025	Elia Bruè Aaron Naber Daniele Semola
+	Stability of tori under lower sectional curvature	2024	Elia Bruè Aaron Naber Daniele Semola
+ PDF Chat	Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature	2024	Gioacchino Antonelli Marco Pozzetta Daniele Semola
+ PDF Chat	Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded below	2024	Elia Bruè Alessandro Pigati Daniele Semola
+	Lecture XVII: The Benamou-Brenier Formula	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture IV: Necessary and Sufficient Optimality Conditions	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture V: Existence of Optimal Maps and Applications	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XI: Gradient Flows: An Introduction	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XVIII: An Introduction to Otto’s Calculus	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture II: The Kantorovich Problem	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XII: Gradient Flows: The Brézis-Komura Theorem	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XIX: Heat Flow, Optimal Transport and Ricci Curvature	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture III: The Kantorovich–Rubinstein Duality	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XIII: Examples of Gradient Flows in PDEs	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture VII: The Monge-Ampére Equation and Optimal Transport on Riemannian Manifolds	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XVI: The Continuity Equation and the Hopf-Lax Semigroup	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture VI: A Proof of the Isoperimetric Inequality and Stability in Optimal Transport	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture X: Wasserstein Geodesics, Nonbranching and Curvature	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lectures on Optimal Transport	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture XV: Semicontinuity and Convexity of Energies in the Wasserstein Space	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture I: Preliminary Notions and the Monge Problem	2024	Luigi Ambrosio Elia Bruè Daniele Semola
+ PDF Chat	Quantitative Obata’s theorem	2023	Fabio Cavalletti Andrea Mondino Daniele Semola
+ PDF Chat	Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds	2023	Gioacchino Antonelli Enrico Pasqualetto Marco Pozzetta Daniele Semola
+ PDF Chat	On the notion of Laplacian bounds on 𝑅𝐶𝐷 spaces and applications	2023	Nicola Gigli Andrea Mondino Daniele Semola
+ PDF Chat	The metric measure boundary of spaces with Ricci curvature bounded below	2023	Elia Bruè Andrea Mondino Daniele Semola
+	On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications	2023	Nicola Gigli Andrea Mondino Daniele Semola
+	Fundamental Groups and the Milnor Conjecture	2023	Elia Bruè Aaron Naber Daniele Semola
+	Stability of Tori under Lower Sectional Curvature	2023	Elia Bruè Aaron Naber Daniele Semola
+	Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces	2023	Francesco Fiorani Andrea Mondino Daniele Semola
+	Six dimensional counterexample to the Milnor Conjecture	2023	Elia Bruè Aaron Naber Daniele Semola
+ PDF Chat	Constancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spaces	2022	Elia Bruè Enrico Pasqualetto Daniele Semola
+	Rectifiability of the reduced boundary for sets of finite perimeter over $\operatorname{RCD}(K,N)$ spaces	2022	Elia Bruè Enrico Pasqualetto Daniele Semola
+ PDF Chat	Boundary regularity and stability for spaces with Ricci bounded below	2022	Elia Bruè Aaron Naber Daniele Semola
+	Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from $\mathrm{RCD}(K,N)$ spaces to $\mathrm{CAT}(0)$ spaces	2022	Andrea Mondino Daniele Semola
+	The metric measure boundary of spaces with Ricci curvature bounded below	2022	Elia Bruè Andrea Mondino Daniele Semola
+	Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds	2022	Gioacchino Antonelli Enrico Pasqualetto Marco Pozzetta Daniele Semola
+	Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds	2022	Gioacchino Antonelli Enrico Pasqualetto Marco Pozzetta Daniele Semola
+ PDF Chat	Improved regularity estimates for Lagrangian flows on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si2.svg"><mml:mrow><mml:mo class="qopname">RCD</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> spaces	2021	Elia Bruè Qin Deng Daniele Semola
+	Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds	2021	Andrea Mondino Daniele Semola
+	Boundary regularity and stability under lower Ricci bounds	2021	Daniele Semola Fanny Bastien Hugo Béchet
+ PDF Chat	Rectifiability of RCD(K,N) spaces via δ-splitting maps	2021	Elia Bruè Enrico Pasqualetto Daniele Semola
+ PDF Chat	The equality case in Cheeger's and Buser's inequalities on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="sans-serif">RCD</mml:mi></mml:math> spaces	2021	Nicolò De Ponti Andrea Mondino Daniele Semola
+	Improved regularity estimates for Lagrangian flows on $\text{RCD}(K,N)$ spaces	2021	Elia Bruè Qin Deng Daniele Semola
+	Lecture 17: The Benamou–Brenier Formula	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 1: Preliminary Notions and the Monge Problem	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 5: Existence of Optimal Maps and Applications	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 13: Examples of Gradient Flows in PDEs	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 2: The Kantorovich Problem	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 9: Analysis on Metric Spaces and the Dynamic Formulation of Optimal Transport	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 16: The Continuity Equation and the Hopf-Lax Semigroup	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 19: Heat Flow, Optimal Transport and Ricci Curvature	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 3: The Kantorovich–Rubinstein Duality	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 4: Necessary and Sufficient Optimality Conditions	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 8: The Metric Side of Optimal Transport	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 12: Gradient Flows: The Brézis-Komura Theorem	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 7: The Monge-Ampére Equation and Optimal Transport on Riemannian Manifolds	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 6: A Proof of the Isoperimetric Inequality and Stability in Optimal Transport	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 10: Wasserstein Geodesics, Nonbranching and Curvature	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 18: An Introduction to Otto’s Calculus	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 15: Semicontinuity and Convexity of Energies in the Wasserstein Space	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Lecture 11: Gradient Flows: An Introduction	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Constancy of the dimension in codimension one and locality of the unit normal on $\mathrm{RCD}(K,N)$ spaces	2021	Elia Bruè Enrico Pasqualetto Daniele Semola
+	Lectures on Optimal Transport	2021	Luigi Ambrosio Elia Bruè Daniele Semola
+	Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds	2021	Andrea Mondino Daniele Semola
+	Rectifiability of RCD(K,N) spaces via $\delta$-splitting maps	2020	Elia Bruè Enrico Pasqualetto Daniele Semola
+	Boundary regularity and stability for spaces with Ricci bounded below	2020	Elia Bruè Aaron Naber Daniele Semola
+	Rectifiability of RCD(K,N) spaces via $δ$-splitting maps	2020	Elia Bruè Enrico Pasqualetto Daniele Semola
+	Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below	2019	Andrea Mondino Daniele Semola
+	Regularity of Lagrangian flows over RCD<sup>*</sup>(<i>K</i>, <i>N</i>) spaces	2019	Elia Bruè Daniele Semola
+	Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces	2019	Gioacchino Antonelli Elia Bruè Daniele Semola
+ PDF Chat	Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces	2019	Luigi Ambrosio Elia Bruè Daniele Semola
+ PDF Chat	Constancy of the Dimension for RCD(<i>K</i>,<i>N</i>) Spaces via Regularity of Lagrangian Flows	2019	Elia Bruè Daniele Semola
+	Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces	2019	Elia Bruè Enrico Pasqualetto Daniele Semola
+ PDF Chat	Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces	2019	Gioacchino Antonelli Elia Bruè Daniele Semola
+	Quantitative Obata's Theorem	2019	Fabio Cavalletti Andrea Mondino Daniele Semola
+	Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces	2019	Gioacchino Antonelli Elia Bruè Daniele Semola
+	Rigidity of the 1-Bakry-\'Emery inequality and sets of finite perimeter in RCD spaces	2018	Luigi Ambrosio Elia Bruè Daniele Semola
+	Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows	2018	Elia Bruè Daniele Semola
+	Regularity of Lagrangian flows over $RCD^*(K,N)$ spaces	2018	Elia Bruè Daniele Semola
+	Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows	2018	Elia Bruè Daniele Semola
+	Rigidity of the 1-Bakry-Émery inequality and sets of finite perimeter in RCD spaces	2018	Luigi Ambrosio Elia Bruè Daniele Semola
+	Regularity of Lagrangian flows over $RCD^*(K,N)$ spaces	2018	Elia Bruè Daniele Semola

Common Coauthors

Coauthor	Papers Together
Elia Bruè	67
Luigi Ambrosio	35
Andrea Mondino	12
Enrico Pasqualetto	10
Aaron Naber	7
Gioacchino Antonelli	7
Marco Pozzetta	4
Luigi Ambrosio	4
Nicola Gigli	2
Fabio Cavalletti	2
Qin Deng	2
Fanny Bastien	1
Francesco Fiorani	1
Nicolò De Ponti	1
Hugo Béchet	1
Alessandro Pigati	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Ricci curvature for metric-measure spaces via optimal transport	2009	John Lott Cédric Villani	25
+ PDF Chat	On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces	2014	Matthias Erbar Kazumasa Kuwada Karl-Theodor Sturm	21
+ PDF Chat	Metric measure spaces with Riemannian Ricci curvature bounded from below	2014	Luigi Ambrosio Nicola Gigli Giuseppe Savaré	20
+ PDF Chat	On the geometry of metric measure spaces. II	2006	Karl‐Theodor Sturm	20
+ PDF Chat	On the differential structure of metric measure spaces and applications	2014	Nicola Gigli	18
+	Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure	2015	Luigi Ambrosio Nicola Gigli Andrea Mondino Tapio Rajala	17
+ PDF Chat	Non-collapsed spaces with Ricci curvature bounded from below	2018	Guido De Philippis Nicola Gigli	16
+	Functions of bounded variation on “good” metric spaces	2003	Michele Miranda	15
+	Optimal Transport: Old and New	2013	Cédric Villani	15
+ PDF Chat	Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows	2015	Nicola Gigli Andrea Mondino Giuseppe Savaré	15
+	Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products	1996	Jeff Cheeger Tobias Colding	14
+ PDF Chat	On the geometry of metric measure spaces	2006	Karl‐Theodor Sturm	14
+ PDF Chat	Structure theory of metric measure spaces with lower Ricci curvature bounds	2019	Andrea Mondino Aaron Naber	14
+	Nonsmooth Differential Geometry: An Approach Tailored for Spaces With Ricci Curvature Bounded from Below	2017	Nicola Gigli	13
+	Localization and tensorization properties of the curvature-dimension condition for metric measure spaces	2010	Kathrin Bacher Karl‐Theodor Sturm	13
+ PDF Chat	On the structure of spaces with Ricci curvature bounded below. I	1997	Jeff Cheeger Tobias Colding	13
+	CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES	2019	Luigi Ambrosio	12
+	Equivalent definitions of BV space and of total variation on metric measure spaces	2014	Luigi Ambrosio Simone Di Marino	12
+	New stability results for sequences of metric measure spaces with uniform Ricci bounds from below	2017	Luigi Ambrosio Shouhei Honda	12
+	Differentiability of Lipschitz Functions on Metric Measure Spaces	1999	Jeff Cheeger	12
+ PDF Chat	Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces	2019	Luigi Ambrosio Andrea Mondino Giuseppe Savaré	12
+ PDF Chat	Well-posedness of Lagrangian flows and continuity equations in metric measure spaces	2014	Luigi Ambrosio Dario Trevisan	11
+ PDF Chat	Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below	2013	Luigi Ambrosio Nicola Gigli Giuseppe Savaré	11
+ PDF Chat	Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below	2017	Luigi Ambrosio Andrea Mondino Giuseppe Savaré	11
+ PDF Chat	On the volume measure of non-smooth spaces with Ricci curvature bounded below	2018	Martin Kell Andrea Mondino	10
+	Optimal Transport	2008	Cédric Villani	10
+ PDF Chat	From volume cone to metric cone in the nonsmooth setting	2016	Guido De Philippis Nicola Gigli	9
+ PDF Chat	Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces	2013	Giuseppe Savaré	9
+ PDF Chat	Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications	2012	Tobias Colding Aaron Naber	9
+ PDF Chat	The globalization theorem for the Curvature-Dimension condition	2021	Fabio Cavalletti Emanuel Milman	9
+	The Globalization Theorem for the Curvature Dimension Condition	2016	Fabio Cavalletti Emanuel Milman	9
+ PDF Chat	Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below	2013	Nicola Gigli Andrea Mondino Tapio Rajala	8
+	Gradient Flows: In Metric Spaces and in the Space of Probability Measures	2005	Luigi Ambrosio Nicola Gigli Giuseppe Savaré	8
+ PDF Chat	Regularity of Einstein manifolds and the codimension 4 conjecture	2015	Jeff Cheeger Aaron Naber	8
+	Independence on p of weak upper gradients on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="sans-serif">RCD</mml:mi></mml:math> spaces	2016	Nicola Gigli Bang-Xian Han	8
+	Ricci Curvature and Volume Convergence	1997	Tobias Colding	7
+ PDF Chat	Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds	2016	Fabio Cavalletti Andrea Mondino	7
+ PDF Chat	Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces	2013	Luigi Ambrosio Nicola Gigli Giuseppe Savaré	7
+ PDF Chat	Heat Kernel Bounds on Metric Measure Spaces and Some Applications	2015	Renjin Jiang Huaiqian Li Hui-Chun Zhang	6
+ PDF Chat	Lower bounds on Ricci curvature and quantitative behavior of singular sets	2012	Jeff Cheeger Aaron Naber	6
+ PDF Chat	Local Poincaré inequalities from stable curvature conditions on metric spaces	2011	Tapio Rajala	6
+	Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below	2021	Jeff Cheeger Wenshuai Jiang Aaron Naber	6
+	Bakry–Émery curvature-dimension condition and Riemannian Ricci curvature bounds	2014	Luigi Ambrosio Nicola Gigli Giuseppe Savaré	6
+ PDF Chat	On the topology and the boundary of N–dimensional RCD(K,N) spaces	2021	Vitali Kapovitch Andrea Mondino	6
+	Rectifiability of Singular Sets in Noncollapsed Spaces with Ricci Curvature bounded below	2018	Jeff Cheeger Wenshuai Jiang Aaron Naber	6
+	Some Nonlinear Problems in Riemannian Geometry	1998	Thierry Aubin	6
+ PDF Chat	Boundary regularity and stability for spaces with Ricci bounded below	2022	Elia Bruè Aaron Naber Daniele Semola	6
+ PDF Chat	On local Poincaré via transportation	2007	Max‐K. von Renesse	6
+	Ordinary differential equations, transport theory and Sobolev spaces	1989	Ronald J. DiPerna Pierre Louis Lions	6
+	Alexandrov meets Lott--Villani--Sturm	2010	Anton Petrunin	6