Variational properties of the total inverse mean curvature in the plane under boundary constraints

2025/10/29 by Pozuelo, Julián, Verzellesi, Simone, Vianello, Giacomo
#49Q10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.25576

Abstract

We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are strongly stable. As an application, we prove a local minimality property.

Citations

• Rigidity of critical points of hydrophobic capillary functionals
• The equality case in the substatic Heintze-Karcher inequality
• New Integral Estimates in Substatic Riemannian Manifolds and the Alexandrov Theorem
• The Heintze-Karcher inequality for metric measure spaces
• An integral formula and its applications on sub-static manifolds
• Constant mean curvature surfaces in warped product manifolds

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