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arXiv · 2510.25576

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

Julián Pozuelo·Simone Verzellesi·Giacomo Vianello
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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.

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Julián Pozuelo, Simone Verzellesi, Giacomo Vianello. 2025-10-29. Variational properties of the total inverse mean curvature in the plane under boundary constraints. https://arxiv.org/abs/2510.25576

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