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Zbl 0641.49028
Esteban, Maria J.
An isoperimetric inequality in ${\bbfR}\sp 3$. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4, 297-305 (1987). ISSN 0294-1449

The classical isoperimetric inequality for domains T in ${\bbfR}\sp 4$ is generalized to the case where the closed hypersurface $S=\partial T$ is given as the image $\Phi ({\bbfR}\sp 3)$ for some $\Phi:{\bbfR}\sp 3\to {\bbfR}\sp 4$. These functions $\Phi$ have to satisfy certain integrability conditions and an approximation property, and the isoperimetric inequality becomes an integral inequality.
[M.Grüter]

MSC 2000:: *49Q20 Variational problems in geometric measure-theoretic setting
26B15 Integration (several real variables)
28A75 Geometric measure theory
49Q15 Geometric measure and integration theory, etc.

Keywords: isoperimetric inequality; integral inequality

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