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

Annales Polonici Mathematici (1996)

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

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topSilvano 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

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

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