## Isoperimetric inequalities in the theory of surfaces of bounded external curvature |

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### Contents

Fundamental Results | 1 |

Extrinsic Curvature | 7 |

Area of a Closed Polyhedral Surface | 17 |

Copyright | |

8 other sections not shown

### Common terms and phrases

According to Lemma analogously angle assertion assume boundary of F bounded curvature Burago Chapter circle clear compact surface components Consequently consider contained converge convex surface corresponding denote diameter endpoints equality equidistants exceed exists face finite number follows Frechet fulfilled geodesic Grassmann manifold Haar measure Hence homeomorphism homotopic hyperplane inequality 1.1 intersect intrinsic geometry intrinsic metric isometric immersions isoperimetric inequalities Lebesgue area Lemma 32 lemma is proved length Let F lune manifold of bounded mapping metric of F moreover nondegenerate nonsingular notation obtain open set pairwise nonintersecting plane polygonal line polyhedral metric polyhedral surface polyhedron positive extrinsic curvature proof of Lemma rectifiable curve rotation saddle surfaces satisfying the condition segment sequence Shefel shortest lines side simple closed curve simplicial parametrization simply-connected region space standard region subsets surface F surface of class surfaces in R2 Theorem 19 triangle truncation upper v-crust valid vertex vertices