Stability of the Wulff shape with respect to anisotropic curvature functionals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913578111467520 |
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| author | Scheuer, Julian Zhang, Xuwen |
| author_facet | Scheuer, Julian Zhang, Xuwen |
| contents | For a function $f$ which foliates a one-sided neighbourhood of a closed hypersurface $M$, we give an estimate of the distance of $M$ to a Wulff shape in terms of the $L^{p}$-norm of the traceless $F$-Hessian of $f$, where $F$ is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15999 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of the Wulff shape with respect to anisotropic curvature functionals Scheuer, Julian Zhang, Xuwen Analysis of PDEs Differential Geometry For a function $f$ which foliates a one-sided neighbourhood of a closed hypersurface $M$, we give an estimate of the distance of $M$ to a Wulff shape in terms of the $L^{p}$-norm of the traceless $F$-Hessian of $f$, where $F$ is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type. |
| title | Stability of the Wulff shape with respect to anisotropic curvature functionals |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2308.15999 |