A. Lytchak, “Open map theorem for metric spaces”, Algebra i Analiz, 17:3 (2005), 139–159; St. Petersburg Math. J., 17:3 (2006), 477

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Algebra i Analiz, 2005, Volume 17, Issue 3, Pages 139–159 (Mi aa673)

This article is cited in 41 scientific papers (total in 41 papers)

Research Papers

Open map theorem for metric spaces

A. Lytchak

Mathematisches Institut, Universität Bonn, Germany

Full-text PDF (1200 kB) Citations (41)

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Abstract: An open map theorem for metric spaces is proved and some applications are discussed. The result on the existence of gradient flows of semiconcave functions is generalized to a large class of spaces.

Keywords: semi-convex functions, Aleksandrov spaces, differentials, gradient flow.

Received: 05.04.2004

English version:
St. Petersburg Mathematical Journal, 2006, Volume 17, Issue 3, Pages 477–491
DOI: https://doi.org/10.1090/S1061-0022-06-00916-2

Bibliographic databases:

Document Type: Article

Language: English

Citation: A. Lytchak, “Open map theorem for metric spaces”, Algebra i Analiz, 17:3 (2005), 139–159; St. Petersburg Math. J., 17:3 (2006), 477–491

Citation in format AMSBIB

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\crossref{https://doi.org/10.1090/S1061-0022-06-00916-2}

Linking options:

https://www.mathnet.ru/eng/aa673

https://www.mathnet.ru/eng/aa/v17/i3/p139

This publication is cited in the following 41 articles:

Karl-Theodor Sturm, “The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces”, Memoirs of the AMS, 290:1443 (2023)
Yin Jiang, “Non-existence of concave functions on certain metric spaces”, Proc. Amer. Math. Soc., 2023
Tadashi Fujioka, “Extremal subsets in geodesically complete spaces with curvature bounded above”, Analysis and Geometry in Metric Spaces, 11:1 (2023)
Nagano K., “Asymptotic Topological Regularity of Cat(0) Spaces”, Ann. Glob. Anal. Geom., 61:2 (2022), 427–457
Peter Petersen, CIMAT Lectures in Mathematical Sciences, Recent Advances in Alexandrov Geometry, 2022, 1
Tadashi Fujioka, “Noncritical maps on geodesically complete spaces with curvature bounded above”, Ann Glob Anal Geom, 62:3 (2022), 661
Tadashi FUJIOKA, “Regular points of extremal subsets in Alexandrov spaces”, J. Math. Soc. Japan, 74:4 (2022)
Moon Duchin, Tom Needham, Thomas Weighill, “The (homological) persistence of gerrymandering”, FoDS, 4:4 (2022), 581
Stadler S., “The Structure of Minimal Surfaces in Cat(0) Spaces”, J. Eur. Math. Soc., 23:11 (2021), 3521–3554
Kapovitch V., Lytchak A., “Remarks on Manifolds With Two-Sided Curvature Bounds”, Anal. Geom. Metr. Spaces, 9:1 (2021), 53–64
Lebedeva N., Ohta Sh.-i., Zolotov V., “Self-Contracted Curves in Spaces With Weak Lower Curvature Bound”, Int. Math. Res. Notices, 2021:11 (2021), 8623–8656
Lytchak A., Petrunin A., “Short Retractions of Cat(1) Spaces”, Proc. Amer. Math. Soc., 149:3 (2021), 1247–1257
Gigli N. Nobili F., “A Differential Perspective on Gradient Flows on Cat(Kappa)-Spaces and Applications”, J. Geom. Anal., 31:12 (2021), 11780–11818
Lange Ch., “Orbifolds From a Metric Viewpoint”, Geod. Dedic., 209:1 (2020), 43–57
Lytchak A., Stadler S., “Improvements of Upper Curvature Bounds”, Trans. Am. Math. Soc., 373:10 (2020), 7153–7166
Muratori M., Savar G., “Gradient Flows and Evolution Variational Inequalities in Metric Spaces. i: Structural Properties”, J. Funct. Anal., 278:4 (2020), UNSP 108347
Ohta Sh.-i., “Self-Contracted Curves in Cat(0)-Spaces and Their Rectifiability”, J. Geom. Anal., 30:1 (2020), 936–967
Kell M., “Sectional Curvature-Type Conditions on Metric Spaces”, J. Geom. Anal., 29:1 (2019), 616–655
Lytchak A. Nagano K., “Geodesically Complete Spaces With An Upper Curvature Bound”, Geom. Funct. Anal., 29:1 (2019), 295–342
Karl-Theodor Sturm, “Gradient flows for semiconvex functions on metric measure spaces – existence, uniqueness, and Lipschitz continuity”, Proc. Amer. Math. Soc., 146:9 (2018), 3985

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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