On totally umbilical surfaces in some Riemannian spaces

Z. Olszak

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In the first part of this paper, we study the best constant involving the L norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes....