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- Title
Weak-strong uniqueness for volume-preserving mean curvature flow.
- Authors
Laux, Tim
- Abstract
In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the concept in the case without volume preservation recently introduced by Fischer, Hensel, Laux and Simon (2021). The first main result shows that any strong solution with certain regularity is calibrated. The second main result consists of a stability estimate in terms of a relative entropy, which is valid in the class of distributional solutions to volume-preserving mean curvature flow.
- Subjects
CURVATURE; RICCI flow; ENTROPY
- Publication
Revista Mathematica Iberoamericana, 2024, Vol 40, Issue 1, p93
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/1395