Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds

DOI10.1007/s00039-020-00522-8zbMath1436.49054arXiv1802.00226OpenAlexW2999069935MaRDI QIDQ2309487

Felix Schulze

Publication date: 1 April 2020

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.00226

zbMATH Keywords

Cartan-Hadamard manifoldsoptimal isoperimetric inequalities

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Currents in global analysis (58A25)

Related Items (6)

Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces ⋮ Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities ⋮ Ancient asymptotically cylindrical flows and applications ⋮ A de Sitter no-hair theorem for 3+1d cosmologies with isometry group forming 2-dimensional orbits ⋮ Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity of area minimizing currents. II: Center manifold
• Regularity of area minimizing currents. III: Blow-up
• Regularity of area minimizing currents I: gradient \(L^p\) estimates
• Optimal rigidity estimates for nearly umbilical surfaces in arbitrary codimension
• Subsequent singularities in mean-convex mean curvature flow
• A sharp four dimensional isoperimetric inequality
• Motion of level sets by mean curvature. I
• A local regularity theorem for mean curvature flow
• Stable branched minimal immersions with prescribed boundary
• Nonlinear evolution by mean curvature and isoperimetric inequalities
• Filling Riemannian manifolds
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• An isoperimetric comparison theorem
• Problèmes isoperimetriques et espaces de Sobolev
• The inverse mean curvature flow and the Riemannian Penrose inequality
• The deformation theorem for flat chains
• Embeddedness of minimal surfaces with total boundary curvature at most \(4\pi\)
• Existence of surfaces minimizing the Willmore functional
• A local regularity theorem for mean curvature flow with triple edges
• The Cartan-Hadamard conjecture and the little prince
• Normal and integral currents
• Isoperimetric inequalities of Euclidean type in metric spaces
• Multiple valued functions and integral currents
• 𝑄-valued functions revisited
• Unique continuation in geometry
• Unique continuation for elliptic operators: A geometric-variational approach
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• A correction to: Sobolev and isoperimetric inequalities for riemannian submanifolds
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Elliptic regularization and partial regularity for motion by mean curvature
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Currents in metric spaces

This page was built for publication: Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds