Hypersurfaces in whose unit normal has small BMO norm

Author:
Stephen Semmes

Journal:
Proc. Amer. Math. Soc. **112** (1991), 403-412

MSC:
Primary 53A05; Secondary 42B99, 53C40

MathSciNet review:
1065093

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Abstract: Let be a hypersurface in whose Gauss map has small BMO norm. This condition is closely related to (but much weaker than) the requirement that the principal curvatures of have small norm. (The relationship between these two conditions is a nonlinear geometrical analogue of a classical Sobolev embedding.) This paper deals with the problem of understanding the geometrical constraints imposed on by the requirement that the Gauss map have small BMO norm.

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1065093-4

Article copyright:
© Copyright 1991
American Mathematical Society