Isoperimetric Inequalities for Parametric Variational Problems
نویسندگان
چکیده
We prove isoperimetric inequalities for general parametric variational double integrals F , whose Lagrangians F depend on the position vector X and on the surface normal N. As an essential tool we introduce Sauvigny’s F -conformal parameters adapted to the parametric integrand and use the notion of generalized mean and Gaussian curvature adapted to the integrand. The special cases of minimal surfaces, surfaces of bounded mean curvature and F-minimizing surfaces are also discussed.
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