Intrinsic Geometry of Surfaces |
Contents
CURVATURE 1 On a method of introducing measure | 1 |
ANGLE | 20 |
CHAPTER III | 43 |
Copyright | |
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absolute curvature absolutely convex adjacent analogous arbitrarily small arbitrary assertion Borel sets boundary bounded curvature bounded variation broken curves Chapter coincide compact complete angle consider construction convex polygon corresponding decomposed defined disc distance endpoints equation excesses excised exists exterior tails Figure finite number follows Gauss-Bonnet theorem geodesic inequality inside interior point intersections intrinsic metric Lemma Lemma 15 length lim inf lim sup lying manifold of bounded metric space Moreover obtain open set pass shortest arcs pasting pieces plane triangle polygonal curves polygons Q polyhedral metric positive curvature proof of Theorem proved reduced triangles region G right rotation rotation of bounded satisfied sector angles segment sequence shortest arc XY sides simple arc simple closed simple polygon simple triangles small neighborhood subdivision subsection Suppose surface t₁ t₂ Theorem 9 triangles homeomorphic two-dimensional manifold two-gon uniform convergence upper angle vertex weak convergence