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math.DG2026
Variation formulas for mean curvature functionals
Simone Verzellesi
We establish first and second variation formulas for general mean curvature functionals under arbitrary variations in arbitrary Riemannian manifolds. We obtain corresponding formul…
math.DG2026
Unexpected phenomena for mean curvature functionals in the Heisenberg group
Mattia Fogagnolo, Andrea Pinamonti, Simone Verzellesi
The Euclidean paradigm that spheres optimize mean curvature variational problems breaks down in the sub-Riemannian Heisenberg group: neither the Pansu sphere nor the Korányi sphere…
math.DG2025
Variational properties of the total inverse mean curvature in the plane under boundary constraints
Julián Pozuelo, Simone Verzellesi, Giacomo Vianello
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 pr…