Axial symmetry for fractional capillarity droplets

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.

Keywords:

• Alexandrov’s theorem
• capillarity problems
• nonlocal perimeter
• symmetry

Acknowledgments

The author would like to thank Francesco Maggi for mentoring, guidance and helpful discussions. They also thank the anonymous referee for carefully reading the paper and for their thoughtful comments.

Additional information

Funding

This work was supported by NSF-DMS Grants 1265910 and 1351122.