arXiv Open Access 2025

Anisotropic fractional area measures

Xiaxing Cai

Lihat Sumber

Abstrak

The anisotropic $s$-fractional area measures are introduced as the first variation of the anisotropic fractional $s$-perimeter $P_s(K,L)$, with $L$ an origin symmetric convex body and $s\in(0,1)$. As $s\rightarrow 1^-$, the anisotropic $s$-fractional area measure converges to the mixed area measure of $K$ and the moment body of $L$. The Minkowski problem of these measures are solved. Finally, a necessary condition for the convexity of optimizers in the anisotropic fractional isoperimetric inequality is derived.

Topik & Kata Kunci

math.MG

Penulis (1)

Xiaxing Cai

Format Sitasi

APA MLA BibTeX

Cai, X. (2025). Anisotropic fractional area measures. https://arxiv.org/abs/2510.05279

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓