{"paper":{"title":"Characterization of balls as minimizers of an endpoint Gagliardo seminorm on the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Mas","submitted_at":"2018-05-09T14:40:23Z","abstract_excerpt":"Given a bounded $C^2$ domain $\\Omega\\subset{\\mathbb R}^d$ with $d\\geq3$, we prove a sharp inequality which relates the perimeter of ${\\partial\\Omega}$ to the endpoint Gagliardo seminorm in $W^{r,2}({\\partial\\Omega})$, corresponding to $r=0$, of the normal vector field on ${\\partial\\Omega}$. The proof of the inequality relies on the use of Bessel potentials and a monotonicity formula; we also show that balls are the unique minimizers. For $1/2<r<1$, the Gagliardo seminorm of the normal vector field on ${\\partial\\Omega}$ is related to a fractional second fundamental form which arises in the stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03557","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}