Intrinsic Diameter and Curvature Integrals of Surfaces Immersed in ℝn

We prove that if Σ is a complete connected surface without boundary smoothly immersed in ℝn, then its intrinsic diameter satisfies the bound diamΣ < Cn volN(Σ), where N(Σ) ⊂ ℝn × Sn−1 is the manifold of unit normals to Σ and Cn is a universal constant depending only on n. In fact we establish a s...

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Veröffentlicht in:	Indiana University mathematics journal 2004-01, Vol.53 (1), p.269-296
1. Verfasser:	Fu, Joseph H.G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Curvature Cylinders Differential geometry Distance functions Exact sciences and technology Geometry Mathematical inequalities Mathematical integrals Mathematical surfaces Mathematical theorems Mathematics Sciences and techniques of general use Topology Trajectories
Online-Zugang:	Volltext
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