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

• Autorzy: Silvano Delladio
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

generalized Gauss graphs; rectifiable currents; generalized curvatures; Meusnier theorem; Fenchel inequality; diameter estimate

Kategorie tematyczne

• 49Q20: Variational problems in a geometric measure-theoretic setting
• 53C65: Integral geometry
• 28A75: Length, area, volume, other geometric measure theory
• 49Q15: Geometric measure and integration theory, integral and normal currents

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 3
• Strony: 267-283

Daty

wydano

1996

otrzymano

1995-08-31

poprawiono

1995-12-20

Twórcy

autor

Silvano Delladio

• Dipartimento di Matemetica, Università di Trento, 38050 Povo (Trento), Italy

Bibliografia

• [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.
• [4] M. W. Hirsch, Differential Topology, Springer, Berlin, 1976.
• [5] F. Morgan, Geometric Measure Theory. A Beginner's Guide, Academic Press, 1988.
• [6] R. Osserman, Curvature in the eighties, Amer. Math. Monthly 97 (1990), 731-756.
• [7] L. Simon, Lectures on Geometric Measure Theory, Proc. Centre Math. Anal. Austral. Nat. Univ. 3, Canberra, 1983.
• [8] L. Simon, Existence of Willmore Surfaces, Proc. Centre Math. Anal. Austral. Nat. Univ. 10, Canberra, 1985.