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A conjecture on minimal surfaces

Gianfranco Cimmino (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Simple computations support the conjecture that a small spherical surface with its center on a minimal surface cannot be divided by the minimal surface into two portions with different area.

A note on the existence of H-bubbles via perturbation methods.

Verónica Felli (2005)

Revista Matemática Iberoamericana

We study the problem of existence of surfaces in R3 parametrized on the sphere S2 with prescribed mean curvature H in the perturbative case, i.e. for H = Ho + EH1, where Ho is a nonzero constant, H1 is a C2 function and E is a small perturbation parameter.

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