Quantitative C¹-stability of spheres in rank one symmetric spaces of non-compact type
METADATA ONLY
Loading...
Author / Producer
Date
2023-04-05
Publication Type
Working Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
We prove that in any rank one symmetric space of non-compact type $M\in\{\mathbb{R} H^n,\mathbb{C} H^m,\mathbb{H} H^m,\mathbb{O} H^2\}$, geodesic spheres are uniformly quantitatively stable with respect to small $C^1$-volume preserving perturbations. We quantify the gain of perimeter in terms of the $W^{1,2}$-norm of the perturbation, taking advantage of the explicit spectral gap of the Laplacian on geodesic spheres in $M$. As a consequence, we give a quantitative proof that for small volumes, geodesic spheres are isoperimetric regions among all sets of finite perimeter.
Permanent link
Publication status
published
Editor
Book title
Journal / series
Volume
Pages / Article No.
2304.02412
Publisher
Cornell University
Event
Edition / version
v1
Methods
Software
Geographic location
Date collected
Date created
Subject
Differential Geometry (math.DG); FOS: Mathematics
Organisational unit
09565 - Figalli, Alessio / Figalli, Alessio
03500 - Lang, Urs / Lang, Urs
Notes
Funding
721675 - Regularity and Stability in Partial Differential Equations (EC)
Related publications and datasets
Is previous version of: