The Library
Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds
Tools
Tools
Tools
Schulze, Felix (2020) Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds. Geometric and Functional Analysis, 30 (1). pp. 255-288. doi:10.1007/s00039-020-00522-8 ISSN 1420-8970.
|
PDF
WRAP-Optimal-isoperimetric-inequalities-Schulze-2020.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (479Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s00039-020-00522-8
Abstract
Let (Mn,g) be simply connected, complete, with non-positive sectional curvatures, and Σ a 2-dimensional closed integral current (or flat chain mod 2) with compact support in M. Let S be an area minimising integral 3-current (resp. flat chain mod 2) such that ∂S=Σ. We use a weak mean curvature flow, obtained via elliptic regularisation, starting from Σ, to show that S satisfies the optimal Euclidean isoperimetric inequality: 6π−−√M[S]≤(M[Σ])3/2. We also obtain an optimal estimate in case the sectional curvatures of M are bounded from above by −κ<0 and characterise the case of equality. The proof follows from an almost monotonicity of a suitable isoperimetric difference along the approximating flows in one dimension higher and an optimal estimate for the Willmore energy of a 2-dimensional integral varifold with first variation summable in L2.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Euclidean algorithm , Integrals , Manifolds (Mathematics) | ||||||||
| Journal or Publication Title: | Geometric and Functional Analysis | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 1420-8970 | ||||||||
| Official Date: | February 2020 | ||||||||
| Dates: |
|
||||||||
| Volume: | 30 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 255-288 | ||||||||
| DOI: | 10.1007/s00039-020-00522-8 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 21 May 2020 | ||||||||
| Date of first compliant Open Access: | 21 May 2020 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
