High-Dimensional Menger-Type Curvatures—Part II: d-Separation and a Menagerie of Curvatures

Gilad Lerman, J. Tyler Whitehouse

Type: Article

Publication Date: 2009-09-29

Citations: 35

DOI: https://doi.org/10.1007/s00365-009-9073-z

View Publication

Locations

Constructive Approximation - View
arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Menger curvature : mathematics, mathematician, dimension	2010	Lambert M. Surhone Miriam T. Timpledon Susan F. Marseken
+	Higher dimensional integral Menger curvature and regularity	2010	Sławomir Kolasiński
+	3. Menger curvature	2002	Hervé Pajot
+	Higher Dimensional Curvatures 2	2023	Xianfeng Gu Emil Saucan
+ PDF Chat	Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part II	2015	Erlend Grong Anton Thalmaier
+	Integral Menger curvature for sets of arbitrary dimension and codimension	2010	Sławomir Kolasiński
+	Curvatures in almost O-spaces	1973	怜古藤
+	Integral Menger curvature for sets of arbitrary dimension and codimension	2010	Sławomir Kolasiński
+	Shorter Notes: Curvature Forms for 2-Manifolds	1970	Nolan R. Wallach F. W. Warner
+	Higher Dimensional Curvatures	2023	Xianfeng Gu Emil Saucan
+	A splitting theorem for spaces of nonpositive curvature	1985	Viktor Schroeder
+	A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications	2009	Ayato Mitsuishi
+ PDF Chat	Quasi-positive curvature and projectivity	2024	Y. J. Du Yanyan Niu
+ PDF Chat	Preserved curvature conditions in higher dimensions	2010	Simon Brendle
+	Integral Menger curvature for sets of arbitrary dimension in $\mathbb{R}^n$. Part I: Uniform Ahlfors regularity	2010	Sławomir Kolasiński
+	Rigidity characterizations of complete Riemannian manifolds with $alpha$-Bach-flat	2021	Guangyue Huang Qianyu Zeng
+	Lower curvature bounds and cohomogeneity one manifolds	2002	Lorenz Schwachhöfer
+	Quasilinearization and curvature of Aleksandrov spaces	2008	Ina Berg Igor Nikolaev
+ PDF Chat	Curvature bounds of subsets in dimension two	2024	Alexander Lytchak Stephan Stadler
+	Riemannian manifolds of quasi-constant sectional curvatures	2000	Georgi Ganchev Vesselka Mihova

Works That Cite This (33)

Action	Title	Year	Authors
+ PDF Chat	Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds	2012	Simon Blatt Sławomir Kolasiński
+	The Singular Strata of a Free-Boundary problem for harmonic measure	2019	Sean McCurdy
+ PDF Chat	Minimal Hölder regularity implying finiteness of integral Menger curvature	2012	Sławomir Kolasiński Marta Szumańska
+ PDF Chat	Symmetrization of a Family of Cauchy-Like Kernels: Global Instability	2022	Loredana Lanzani Malabika Pramanik
+	On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-semimetrics and simplex-type inequalities for high-dimensional sine functions	2008	Gilad Lerman J. Tyler Whitehouse
+ PDF Chat	Regularizing and self-avoidance effects of integral Menger curvature	2010	Paweł Strzelecki Szumańska Marta Heiko von der Mosel
+	Integral Menger curvature for surfaces	2010	Paweł Strzelecki Heiko von der Mosel
+	Local scales on curves and surfaces	2012	Triet Le Facundo Mémoli
+	How nice are critical knots? Regularity theory for knot energies	2014	Simon Blatt Philipp Reiter
+ PDF Chat	Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability	2022	Giacomo Del Nin Kennedy Obinna Idu

Works Cited by This (19)

Action	Title	Year	Authors
+	Big-Pieces-of-Lipschitz-Images Implies a Sufficient Carleson Estimate in a Metric Space	2007	Raanan Schul
+	Untersuchungen über allgemeine Metrik. Vierte Untersuchung. Zur Metrik der Kurven.	2002	Karl Menger
+	On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-semimetrics and simplex-type inequalities for high-dimensional sine functions	2008	Gilad Lerman J. Tyler Whitehouse
+	Gromov hyperbolic spaces	2005	Jussi Väısälä
+ PDF Chat	Menger curvature and Lipschitz parametrizations in metric spaces	2005	Immo Hahlomaa
+	Rectifiable sets and the Traveling Salesman Problem	1990	Peter W. Jones
+ PDF Chat	Bi-Lipschitz decomposition of Lipschitz functions into a metric space	2009	Raanan Schul
+	Untersuchungen über allgemeine Metrik	2002	Karl Menger
+	Quantifying curvelike structures of measures by using <i>L</i><sub>2</sub> Jones quantities	2003	Gilad Lerman
+ PDF Chat	Bilipschitz embeddings of metric spaces into Euclidean spaces	1999	Stephen Semmes