Axial symmetry for fractional capillarity droplets

TL;DR

This paper extends classical symmetry results for capillarity droplets to the fractional mean curvature setting, showing that certain hypersurfaces exhibit axial symmetry under analogous conditions.

Contribution

It proves an axial symmetry result for hypersurfaces with fractional mean curvature, generalizing Wente's classical result to nonlocal curvature operators.

Findings

Establishes axial symmetry for fractional mean curvature hypersurfaces

Generalizes classical capillarity symmetry results to nonlocal operators

Provides mathematical framework for fractional capillarity droplet analysis

Abstract

A classical result of Wente, motivated by the study of sessile capillarity droplets, demonstrates the axial symmetry of every hypersurface which meets a hyperplane at a constant angle and has mean curvature dependent only on the distance from that hyperplane. An analogous result is proven here for the fractional mean curvature operator.