On the regularity of Alexandrov surfaces with curvature bounded below

DOI10.1515/agms-2016-0012zbMath1353.53018OpenAlexW2555359256WikidataQ125911407 ScholiaQ125911407MaRDI QIDQ2520425

Jérôme Bertrand, Luigi Ambrosio

Publication date: 13 December 2016

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/agms-2016-0012

zbMATH Keywords

Alexandrov spacessurfaces with bounded integral curvaturepotential theory on surfaces

Mathematics Subject Classification ID

Metric geometry (51F99) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Methods of local Riemannian geometry (53B21)

Related Items (8)

Metric-measure boundary and geodesic flow on Alexandrov spaces ⋮ Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ Triangulating metric surfaces ⋮ Asymptotically mean value harmonic functions in subriemannian and RCD settings ⋮ Optimal diameter estimate of three-dimensional Ricci limit spaces ⋮ On 3-manifolds with pointwise pinched nonnegative Ricci curvature ⋮ Boundary structure of convex sets in the hyperbolic space ⋮ DC calculus

Cites Work

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• Zum potentialtheoretischen Aspekt der Alexandrowschen Flächentheorie
• A concentration-compactness principle for sequences of Riemannian surfaces.
• A geometrical approach to monotone functions in \(\mathbb{R}^n\)
• The Gaussian curvature of Alexandrov surfaces
• The Riemannian structure of Alexandrov spaces
• Einstein manifolds
• A.D. Alexandrov spaces with curvature bounded below

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