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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A remark on the nonuniqueness of tangent cones


Authors: John E. Hutchinson and Michael Meier
Journal: Proc. Amer. Math. Soc. 97 (1986), 184-185
MSC: Primary 49F20
DOI: https://doi.org/10.1090/S0002-9939-1986-0831410-9
MathSciNet review: 831410
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Abstract: We give an example of an $ n$-dimensional varifold $ V$ such that the $ n$-dimensional density of $ V$ at some point $ p$ equals 1, the $ (n - 1)$ density of the first variation at $ p$ equals 0, and $ V$ has nonunique tangent cones at $ p$. This answers the question implicit in [W. Allard, On the first variation of a varifold, Ann. of Math. (2) 95 (1972), 417-491, §6.5].


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DOI: https://doi.org/10.1090/S0002-9939-1986-0831410-9
Article copyright: © Copyright 1986 American Mathematical Society