On uniqueness of graphs with constant mean curvature

• Autores: Rafael López Camino
• Localización: Journal of mathematics of Kyoto University, ISSN 0023-608X, Vol. 46, Nº 4, 2006, págs. 771-787
• Idioma: inglés
• DOI: 10.1215/kjm/1250281603
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• Resumen

  • A result due to Serrin assures that a graph with constant mean curvature $H \neq 0$ in Euclidean space $\mathbb{R}^{3}$ cannot keep away a distance $1/|H|$ from its boundary. When the distance is exactly $1/|H|$, then the surface is a hemisphere. Following ideas due to Meeks, in this note we treat the aspect of the equality in the Serrin�s estimate as well as generalizations in other situations and ambient spaces.