Year: 2026
Type: preprint
Abstract: We show that the fractional Michael-Simon inequality does not hold for general smooth hypersurfaces and for the range of 0 < s < (n-1)/n in the case p=1. We construct a family of smooth hypersurfaces, whose fractional mean curvature is nonnegative everywhere, which violates the inequality in the limit. The same construction yields a counterexample for every 1 \leq p < \infty for the range s < (n-1)/(np).
Source: arXiv (Cornell University)
Authors: Julin, Vesa, Palatucci, Giampiero
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223096678