Relative isoperimetric inequality on a curved surface
Seo, Keomkyo
J. Math. Kyoto Univ., Tome 46 (2006) no. 4, p. 525-533 / Harvested from Project Euclid
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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.
Publié le : 2006-05-15
Classification:  58E35,  49K10,  49Q20,  53A05 
@article{1250281747,
     author = {Seo, Keomkyo},
     title = {Relative isoperimetric inequality on a curved surface},
     journal = {J. Math. Kyoto Univ.},
     volume = {46},
     number = {4},
     year = {2006},
     pages = { 525-533},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250281747}
}

Seo, Keomkyo. Relative isoperimetric inequality on a curved surface. J. Math. Kyoto Univ., Tome 46 (2006) no. 4, pp.  525-533. http://gdmltest.u-ga.fr/item/1250281747/