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Hypersurfaces in Rn Whose Unit Normal has Small BMO Norm

Stephen Semmes
Proceedings of the American Mathematical Society
Vol. 112, No. 2 (Jun., 1991), pp. 403-412
DOI: 10.2307/2048733
Stable URL: http://www.jstor.org/stable/2048733
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hypersurfaces in Rn Whose Unit Normal has Small BMO Norm
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Abstract

Let M be a hypersurface in Rd + 1 whose Gauss map has small BMO norm. This condition is closely related to (but much weaker than) the requirement that the principal curvatures of M have small Ld(M) 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 M by the requirement that the Gauss map have small BMO norm.

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