منابع مشابه
Extrinsic Curvature of Semiconvex Subspaces in Alexandrov Geometry
In Alexandrov spaces of curvature bounded either above (CBA) or below (CBB), we obtain extrinsic curvature bounds on subspaces associated with semiconcave functions. For CBA spaces, we obtain new intrinsic curvature bounds on subspaces. For CBB spaces whose boundary is extrinsically curved, we strengthen Perelman’s concavity theorem for distance from the boundary, deriving corollaries on sharp ...
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We call A ⊂ RN intervally thin if for all x, y ∈ RN and ε > 0 there exist x′ ∈ B(x, ε), y′ ∈ B(y, ε) such that [x′, y′] ∩ A = ∅. Closed intervally thin sets behave like sets with measure zero (for example such a set cannot ”disconnect” an open connected set). Let us also mention that if the (N − 1)-dimensional Hausdorff measure of A is zero, then A is intervally thin. A function f is preconvex ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1981
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700017973