eprintid: 10089257
rev_number: 30
eprint_status: archive
userid: 608
dir: disk0/10/08/92/57
datestamp: 2020-01-10 14:27:30
lastmod: 2020-11-19 12:24:06
status_changed: 2020-06-04 11:19:53
type: article
metadata_visibility: show
creators_name: Schulze, F
title: Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds
ispublished: pub
divisions: UCL
divisions: A01
divisions: B04
divisions: C06
divisions: F59
note: This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
date: 2020-02
date_type: published
publisher: Springer Verlag
official_url: https://doi.org/10.1007/s00039-020-00522-8
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1738696
doi: 10.1007/s00039-020-00522-8
lyricists_name: Schulze, Felix
lyricists_id: FSCHU22
actors_name: Schulze, Felix
actors_id: FSCHU22
actors_role: owner
full_text_status: public
publication: Geometric and Functional Analysis
volume: 30
pagerange: 255-288
citation:        Schulze, F;      (2020)    Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds.                   Geometric and Functional Analysis , 30    pp. 255-288.    10.1007/s00039-020-00522-8 <https://doi.org/10.1007/s00039-020-00522-8>.       Green open access   
 
document_url: https://discovery-pp.ucl.ac.uk/id/eprint/10089257/1/Schulze_Schulze2020_Article_OptimalIsoperimetricInequaliti.pdf