Slicing of generalized surfaces with curvature measures and diameter's estimate

Silvano Delladio

Annales Polonici Mathematici (1996)

  • Volume: 64, Issue: 3, page 267-283
  • ISSN: 0066-2216

Abstract

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We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.

How to cite

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Silvano Delladio. "Slicing of generalized surfaces with curvature measures and diameter's estimate." Annales Polonici Mathematici 64.3 (1996): 267-283. <http://eudml.org/doc/270023>.

@article{SilvanoDelladio1996,
abstract = {We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.},
author = {Silvano Delladio},
journal = {Annales Polonici Mathematici},
keywords = {generalized Gauss graphs; rectifiable currents; generalized curvatures; Meusnier theorem; Fenchel inequality; diameter estimate; Meusier's theorem; Fenchel's inequality},
language = {eng},
number = {3},
pages = {267-283},
title = {Slicing of generalized surfaces with curvature measures and diameter's estimate},
url = {http://eudml.org/doc/270023},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Silvano Delladio
TI - Slicing of generalized surfaces with curvature measures and diameter's estimate
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 3
SP - 267
EP - 283
AB - We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.
LA - eng
KW - generalized Gauss graphs; rectifiable currents; generalized curvatures; Meusnier theorem; Fenchel inequality; diameter estimate; Meusier's theorem; Fenchel's inequality
UR - http://eudml.org/doc/270023
ER -

References

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  1. [1] G. Anzellotti, R. Serapioni and I. Tamanini, Curvatures, functionals, currents, Indiana Univ. Math. J. 39 (1990), 617-669. 
  2. [2] M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976. 
  3. [3] H. Federer, Geometric Measure Theory, Springer, Berlin, 1969. Zbl0176.00801
  4. [4] M. W. Hirsch, Differential Topology, Springer, Berlin, 1976. 
  5. [5] F. Morgan, Geometric Measure Theory. A Beginner's Guide, Academic Press, 1988. Zbl0671.49043
  6. [6] R. Osserman, Curvature in the eighties, Amer. Math. Monthly 97 (1990), 731-756. Zbl0722.53001
  7. [7] L. Simon, Lectures on Geometric Measure Theory, Proc. Centre Math. Anal. Austral. Nat. Univ. 3, Canberra, 1983. Zbl0546.49019
  8. [8] L. Simon, Existence of Willmore Surfaces, Proc. Centre Math. Anal. Austral. Nat. Univ. 10, Canberra, 1985. 

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