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Oriented and nonoriented curvature varifolds

Published online by Cambridge University Press:  14 November 2011

S. Delladio  and
G. Scianna
S. Delladio
Affiliation:
Dipartimento di Matematica, Universitá di Trento, 38050 Povo, Italy
G. Scianna
Affiliation:
Dipartimento di Matematica, Universitá di Siena, 53100 Siena, Italy
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Abstract

In a recent work, G. Anzellotti and the present authors introduced a notion of variation for functions defined over a rectifiable current. In this paper, we give a definition of a curvature varifold slightly different from that of Hutchinson (equivalent in the nonoriented case) and we study the variation properties, in the sense of [2], of the normal to a rectifiable current when the associated varifold is a curvature varifold.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 1 , 1995 , pp. 63 - 83
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Allard, W. K.. On the first variation of a varifold. Ann. of Math. 95 (1972), 417–491.CrossRefGoogle Scholar
2Anzellotti, G., Delladio, S. and Scianna, G.. BV functions over rectifiable currents. Annali Mat. Pura Appl., Bologna (submitted).Google Scholar
3Anzellotti, G., Serapioni, R. and Tamanini, I.. Curvature, functionals, currents. Indiana Univ. Math. J. 39(1990), 617–669.CrossRefGoogle Scholar
4Federer, H.. Geometric Measure Theory (Berlin: Springer, 1969).Google Scholar
5Hutchinson, J. E.. Second fundamental form for varifolds and the existence of surfaces minimising curvature. Indiana Univ. Math. J. 35 (1986), 45–71.CrossRefGoogle Scholar
6Simon, L.. Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis 3 (Canberra: Australian National University, 1984).Google Scholar