Relative isoperimetric inequality on a curved surface

• Autores: Keomkyo Seo
• Localización: Journal of mathematics of Kyoto University, ISSN 0023-608X, Vol. 46, Nº 3, 2006, págs. 525-533
• Idioma: inglés
• DOI: 10.1215/kjm/1250281747
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• Resumen

  • Let $C$ be a closed convex set on a complete simply connected surface $S$ whose Gaussian curvature is bounded above by a nonpositive constant $K$. For a relatively compact subset $\Omega \subset S \sim C$, we obtain the sharp relative isoperimeric inequality $2\pi \mathrm{Area}(\Omega )-K\mathrm{Area}(\Omega )^{2} \leq \mathrm{Length}(\partial \Omega \sim \partial C)^{2}$. And we also have a similar partial result with positive Gaussian curvature bound.