Stephanie Alexander

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All published works

Action	Title	Year	Authors
+	Dimension of CAT spaces	2024	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Polyhedral spaces	2024	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Ultralimits	2024	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Alexandrov Geometry	2024	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+ PDF Chat	Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theorems	2023	Stephanie Alexander Melanie Graf Michael Kunzinger Clemens Sämann
+	On Taking Time Seriously (1914)	2021	Stephanie Alexander
+	Alexandrov geometry: preliminary version no. 1	2019	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Gluing theorem and billiards	2019	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Globalization and asphericity	2019	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theorems	2019	Stephanie Alexander Melanie Graf Michael Kunzinger Clemens Sämann
+ PDF Chat	An Invitation to Alexandrov Geometry	2019	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+ PDF Chat	Convex functions and geodesic connectedness of space-times	2017	Stephanie Alexander William A. Karr
+	Space-time convex functions and sectional curvature	2017	Stephanie Alexander William A. Karr
+	Invitation to Alexandrov geometry: CAT[0] spaces	2017	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+ PDF Chat	Space-Time Convex Functions and Sectional Curvature	2017	Stephanie Alexander William A. Karr
+	Space-time convex functions and sectional curvature	2017	Stephanie Alexander William A. Karr
+	Warped products admitting a curvature bound	2016	Stephanie Alexander Richard L. Bishop
+	Convex Functions and Geodesic Connectedness of Space-times	2015	Stephanie Alexander William A. Karr
+	Warped products admitting a curvature bound	2015	Stephanie Alexander Richard L. Bishop
+	Convex Functions and Geodesic Connectedness of Space-times	2015	Stephanie Alexander William A. Karr
+	Warped products admitting a curvature bound	2015	Stephanie Alexander Richard L. Bishop
+	An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds	2013	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+ PDF Chat	Topology of Riemannian submanifolds with prescribed boundary	2010	Stephanie Alexander Mohammad Ghomi Jeremy Wong
+ PDF Chat	Total curvature and simple pursuit on domains of curvature bounded above	2010	Stephanie Alexander Bishop R Robert Ghrist
+	Alexandrov meets Kirszbraun	2010	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+ PDF Chat	Extrinsic curvature of semiconvex subspaces in Alexandrov geometry	2009	Stephanie Alexander Richard L. Bishop
+	Total curvature and simple pursuit on domains of curvature bounded above	2009	Stephanie Alexander Bishop R Robert Ghrist
+ PDF Chat	An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds	2008	Stephanie Alexander Vitali Kapovitch Anton Petrunin
+	Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds	2008	Stephanie Alexander Richard L. Bishop
+ PDF Chat	Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds	2008	Stephanie Alexander Richard L. Bishop
+ PDF Chat	Gauss Equation And Injectivity Radii For Subspaces in Spaces of Curvature Bounded Above	2006	Stephanie Alexander Richard L. Bishop
+ PDF Chat	A cone splitting theorem for Alexandrov spaces	2005	Stephanie Alexander Richard L. Bishop
+	Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above	2005	Stephanie Alexander Richard L. Bishop
+	Curvature bounds for warped products of metric spaces	2004	Stephanie Alexander Richard L. Bishop
+ PDF Chat	The convex hull property of noncompact hypersurfaces with positive curvature	2004	Stephanie Alexander Mohammad Ghomi
+ PDF Chat	Spines and topology of thin Riemannian manifolds	2003	Stephanie Alexander Richard L. Bishop
+	The convex hull property and topology of hypersurfaces with nonnegative curvature	2003	Stephanie Alexander Mohammad Ghomi
+	? K -convex functions on metric spaces	2003	Stephanie Alexander Richard L. Bishop
+	Spines and Homology of Thin Riemannian Manifolds with Boundary	2000	Stephanie Alexander Richard L. Bishop
+	Warped products of Hadamard spaces	1998	Stephanie Alexander Richard L. Bishop
+	Thin Riemannian manifolds with boundary	1998	Stephanie Alexander Richard L. Bishop
+ PDF Chat	The Fary-Milnor theorem in Hadamard manifolds	1998	Stephanie Alexander Richard L. Bishop
+	None	1997	Stephanie Alexander Richard L. Bishop
+	Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above	1996	Stephanie Alexander Richard L. Bishop
+ PDF Chat	Geometric Curvature Bounds in Riemannian Manifolds with Boundary	1993	Stephanie Alexander I. David Berg Richard L. Bishop
+ PDF Chat	Geometric curvature bounds in Riemannian manifolds with boundary	1993	Stephanie Alexander Ina Berg Richard L. Bishop
+ PDF Chat	Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary.	1993	Stephanie Alexander Ina Berg Richard L. Bishop
+	The distance-geometry of Riemannian manifolds with boundary	1993	Stephanie Alexander I. David Berg Richard L. Bishop
+	Hypersurfaces and nonnegative curvature	1993	Stephanie Alexander Robert Currier
+	Non-Negatively Curved Hypersurfaces of Hyperbolic Space and Subharmonic Functions	1990	Stephanie Alexander Robert J. Currier
+ PDF Chat	The Riemannian obstacle problem	1987	Stephanie Alexander Ina Berg Richard L. Bishop
+	Cauchy uniqueness in the Riemannian obstacle problem	1986	Stephanie Alexander Ina Berg Richard L. Bishop
+	Distance geometry in Riemannian manifolds-with-boundary	1981	Stephanie Alexander
+ PDF Chat	Local and global convexity in complete Riemannian manifolds	1978	Stephanie Alexander
+ PDF Chat	Cylindricity of isometric immersions between hyperbolic spaces	1978	Stephanie Alexander Esther Portnoy
+ PDF Chat	Locally convex hypersurfaces of negatively curved spaces	1977	Stephanie Alexander
+ PDF Chat	Isometric immersions of Riemannian products in Euclidean space	1976	Stephanie Alexander Robert Maltz
+ PDF Chat	Convex-supporting domains on spheres	1974	Stephanie Alexander Richard L. Bishop
+ PDF Chat	Prolongations and completions of Riemannian manifolds	1972	Stephanie Alexander Richard L. Bishop
+	Mathematical Space and Time	1966	Stephanie Alexander
+	Perspectives and Sections of Physical Space-Time	1966	Stephanie Alexander

Common Coauthors

Coauthor	Papers Together
Richard L. Bishop	26
Vitali Kapovitch	12
Anton Petrunin	12
William A. Karr	6
Ina Berg	4
Mohammad Ghomi	3
Clemens Sämann	2
Melanie Graf	2
I. David Berg	2
Robert Ghrist	2
Robert Currier	2
Bishop R	2
Michael Kunzinger	2
Esther Portnoy	1
Robert Maltz	1
Jeremy Wong	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Metric Spaces of Non-Positive Curvature	1999	Martin R. Bridson André Haefliger	15
+	A Course in Metric Geometry	2001	Dmitri Burago Yuri Burago S. V. Ivanov	12
+	Curvature bounds for warped products of metric spaces	2004	Stephanie Alexander Richard L. Bishop	9
+	? K -convex functions on metric spaces	2003	Stephanie Alexander Richard L. Bishop	8
+ PDF Chat	Lectures on Spaces of Nonpositive Curvature	1995	Werner Ballmann	8
+	Hyperbolic Manifolds, Groups and Actions	1981	M. Gromov	8
+ PDF Chat	The Riemannian obstacle problem	1987	Stephanie Alexander Ina Berg Richard L. Bishop	7
+ PDF Chat	Geometric curvature bounds in Riemannian manifolds with boundary	1993	Stephanie Alexander Ina Berg Richard L. Bishop	7
+	Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above	1996	Stephanie Alexander Richard L. Bishop	7
+	A.D. Alexandrov spaces with curvature bounded below	1992	Yu. D. Burago M. Gromov G. Perelman	7
+	Metric Spaces of Curvature ⩾ k	2001	Conrad Plaut	6
+	Nonpositive Curvature: Geometric and Analytic Aspects	1997	Jürgen Jost	6
+ PDF Chat	Semiconcave Functions in Alexandrov’s Geometry	2006	Anton Petrunin	6
+ PDF Chat	Comparison and rigidity theorems in semi-Riemannian geometry	1998	Lars Andersson Ralph Howard	6
+ PDF Chat	On the Structure of Complete Manifolds of Nonnegative Curvature	1972	Jeff Cheeger Detlef Gromoll	6
+	Manifolds of Nonpositive Curvature	1985	Werner Ballmann Mikhael Gromov Viktor Schroeder	5
+	Warped products of Hadamard spaces	1998	Stephanie Alexander Richard L. Bishop	5
+	On Hypersurfaces with no Negative Sectional Curvatures	1960	Richard Sacksteder	5
+	Multidimensional Generalized Riemannian Spaces	1993	V. N. Berestovskij Igor Nikolaev	5
+ PDF Chat	Warped products of metric spaces of curvature bounded from above	1999	Chien Hsiung Chen	5
+	On Spherical Image Maps Whose Jacobians Do Not Change Sign	1959	Philip Hartman Louis Nirenberg	5
+ PDF Chat	Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds	2008	Stephanie Alexander Richard L. Bishop	5
+	Kirszbraun's Theorem and Metric Spaces of Bounded Curvature	1997	Urs Lang Viktor Schroeder	4
+	On the geometry of subsets of positive reach	2004	Alexander Lytchak	4
+	Global Lorentzian Geometry	2017	John K. Beem Paul E. Ehrlich Kevin L. Easley	4
+	Generalized Riemannian spaces	1986	A. D. Aleksandrov V. N. Berestovskiĭ Igor Nikolaev	4
+	Metric minimizing surfaces	1999	Anton Petrunin	4
+	Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one	1992	M. Gromov Richard Schoen	4
+ PDF Chat	Open map theorem for metric spaces	2006	Alexander Lytchak	4
+ PDF Chat	Convex functions and spacetime geometry	2001	G. W. Gibbons Akihiro Ishibashi	4
+	On locally convex manifolds	1952	John van Heijenoort	4
+	A Morse theory for geodesics on a Lorentz manifold	1975	Karen Uhlenbeck	4
+	General theory of irregular curves	1989	Yu. G. Reshetnyak V. V. Alexandrov	4
+	Gap theorems for noncompact Riemannian manifolds	1982	Robert E. Greene H. Wu	4
+ PDF Chat	Manifolds of negative curvature	1969	Richard L. Bishop Barrett O’Neill	4
+ PDF Chat	Differentiation in metric spaces	2005	Alexander Lytchak	3
+ PDF Chat	An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds	2008	Stephanie Alexander Vitali Kapovitch Anton Petrunin	3
+ PDF Chat	The curvature of minimal surfaces in singular spaces	2001	Chikako Mese	3
+	The local structure of length spaces with curvature bounded above	1999	Bruce Kleiner	3
+ PDF Chat	A convergence theorem for Riemannian submanifolds	1995	Zhong Min Shen	3
+	Nonnegatively curved ends of Euclidean hypersurfaces	1991	StephanieB. Alexander Robert J. Currier	3
+ PDF Chat	A globalization for non-complete but geodesic spaces	2015	Anton Petrunin	3
+ PDF Chat	The splitting theorem for manifolds of nonnegative Ricci curvature	1971	Jeff Cheeger Detlef Gromoll	3
+ PDF Chat	The length of a curve in a space of curvature ≤𝐾	1980	B. V. Dekster	3
+	Asymptotic invariants of infinite groups	1993	Mikhael Gromov Graham A. Niblo Martin A. Roller	3
+ PDF Chat	Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings	1997	Bruce Kleiner Bernhard Leeb	3
+ PDF Chat	CAT(κ)-Spaces: Construction and Concentration	2003	M. Gromov	3
+ PDF Chat	Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature	2001	Mohammad Ghomi	3
+ PDF Chat	A cone splitting theorem for Alexandrov spaces	2005	Stephanie Alexander Richard L. Bishop	3
+	Inextensible mappings in a space of curvature no greater than K	1968	Yu. G. Reshetnyak	3