Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball

On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces

In this note we prove a localized form of Alexandrov-Fenchel inequality for convex bodies, i.e. we prove a class of isoperimetric inequalities in a ball involving Federer curvature measures. 1991 Mathematics Subject Classification: 52A20, 52A39, 52A40, 49Q15.

Alexandrov Curvature of Convex Hypersurfaces in Hilbert Space Forms

It is shown that convex hypersurfaces in Hilbert space forms have corresponding lower bounds on Alexandrov curvature. This extends earlier work of Buyalo, Alexander, Kapovitch, and Petrunin for convex hypersurfaces in Riemannian manifolds of finite dimension.

A Form of Alexandrov - Fenchel Inequalitypengfei Guan

On Locally Convex Hypersurfaces with Boundary

In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for ...

Wolff’s inequality for hypersurfaces

We extend Wolff’s “local smoothing” inequality [18] to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature, as well as certain surfaces with more than one flat direction. An immediate consequence is the Lp-boundedness of the corresponding Fourier multiplier operators. Mathematics Subject Classification: 42B08, 42B15. ...