Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms

DOI10.1007/s00526-015-0898-yzbMath1357.53041arXiv1501.04886OpenAlexW1935822625WikidataQ115387345 ScholiaQ115387345MaRDI QIDQ889747

César Rosales, Ana Hurtado

Publication date: 9 November 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.04886

zbMATH Keywords

isoperimetric problemarea functionalWebster curvaturecontact sub-Riemannian manifoldSasakian sub-Riemannian manifold

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Sub-Riemannian geometry (53C17)

Related Items (4)

Cauchy's surface area formula in the Heisenberg groups ⋮ Area-minimizing properties of Pansu spheres in the sub-Riemannian 3-sphere ⋮ An instability criterion for volume-preserving area-stationary surfaces with singular curves in sub-Riemannian 3-space forms ⋮ Strongly stable surfaces in sub-Riemannian 3-space forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the classification of complete area-stationary and stable surfaces in the subriemannian sol manifold
• Rearrangements in metric spaces and in the Heisenberg group
• Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds
• A characteristic property of spheres
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Existence and uniqueness for \(p\)-area minimizers in the Heisenberg group
• Hypersurfaces and variational formulas in sub-Riemannian Carnot groups
• Area-stationary and stable surfaces of class \(C^1\) in the sub-Riemannian Heisenberg group \(\mathbb{H}^1\)
• Constant mean curvature surfaces in sub-Riemannian geometry
• Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\)
• The classification of complete stable area-stationary surfaces in the Heisenberg group
• Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity
• Regularity of \(C^{1}\) smooth surfaces with prescribed \(p\)-mean curvature in the Heisenberg group
• Hopf tori in \(S^ 3\)
• Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
• The classification of simply-connected contact sub-Riemannian symmetric spaces
• Differential forms on contact manifolds
• Umbilicity and characterization of Pansu spheres in the Heisenberg group
• Existence of isoperimetric regions in contact sub-Riemannian manifolds
• The geometric Sobolev embedding for vector fields and the isoperimetric inequality
• Sub-Riemannian homogeneous spaces in dimensions 3 and 4
• First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds
• Stable \(H\)-minimal hypersurfaces
• Sub-Riemannian calculus on hypersurfaces in Carnot groups
• A proof by calibration of an isoperimetric inequality in the Heisenberg group \({\mathbb{H}}^{n}\)
• Area-stationary surfaces inside the sub-Riemannian three-sphere
• \(H\)-minimal graphs of low regularity in \(\mathbb H^1\)
• On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\)
• Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group \(\mathbb H^n\)
• The topology of contact Riemannian manifolds
• Sasakian manifolds with constant \(\phi\)-holomorphic sectional curvature
• The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
• Properly embedded and immersed minimal surfaces in the Heisenberg group
• A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
• Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group
• Isoperimetric inequalities & volume comparison theorems on CR manifolds
• Size of characteristic sets and functions with prescribed gradient
• Analytic Inequalities
• Riemannian geometry of contact and symplectic manifolds
• Sur un théorème de traces. (On a trace theorem)
• Rectifiability and perimeter in the Heisenberg group

This page was built for publication: Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms