Smooth Measures

2013 ◽  
pp. 261-303
Author(s):  
Luis Barreira ◽  
Yakov Pesin
Keyword(s):  
Smooth Measures

Hahn-Jordan decomposition for smooth measures

1981 ◽  
Vol 30 (3) ◽  
pp. 710-712
Author(s):  
E. T. Shavgulidze
Keyword(s):  
Jordan Decomposition ◽  
Smooth Measures

The Converse Fatou Theorem for Smooth Measures

2006 ◽  
Vol 134 (4) ◽  
pp. 2288-2291
Author(s):  
E. S. Dubtsov
Keyword(s):  
Fatou Theorem ◽  
Smooth Measures

Factorization of smooth measures

1990 ◽  
Vol 48 (5) ◽  
pp. 1158-1162 ◽  
Author(s):  
A. V. Uglanov
Keyword(s):  
Smooth Measures

Anisotropic Gauss curvature flows and their associated Dual Orlicz-Minkowski problems

2021 ◽  
pp. 1-15
Author(s):  
Li Chen
Keyword(s):  
Type Equation ◽  
Gauss Curvature ◽  
Curvature Flow ◽  
Strictly Convex ◽  
Convex Solution ◽  
Orlicz Minkowski Problem ◽  
Closed Hypersurfaces ◽  
Smooth Measures ◽  
Gauss Curvature Flow ◽  
Monge Ampere

In this paper we study a normalized anisotropic Gauss curvature flow of strictly convex, closed hypersurfaces in the Euclidean space. We prove that the flow exists for all time and converges smoothly to the unique, strictly convex solution of a Monge-Ampère type equation and we obtain a new existence result of solutions to the Dual Orlicz-Minkowski problem for smooth measures, especially for even smooth measures.

The Fourier Transforms of Smooth Measures on Hypersurfaces of Rn + 1

1986 ◽  
Vol 38 (2) ◽  
pp. 328-359 ◽  
Author(s):  
Bernard Marshall
Keyword(s):  
Fourier Transform ◽  
Asymptotic Expansion ◽  
Unit Sphere ◽  
Gaussian Curvature ◽  
Fourier Transforms ◽  
Surface Measure ◽  
Positive Gaussian Curvature ◽  
Smooth Measures ◽  
The Fourier Transform ◽  
Image Position

The Fourier transform of the surface measure on the unit sphere in Rn + 1, as is well-known, equals the Bessel functionIts behaviour at infinity is described by an asymptotic expansionThe purpose of this paper is to obtain such an expression for surfaces Σ other than the unit sphere. If the surface Σ is a sufficiently smooth compact n-surface in Rn + 1 with strictly positive Gaussian curvature everywhere then with only minor changes in the main term, such an asymptotic expansion exists. This result was proved by E. Hlawka in [3]. A similar result concerned with the minimal smoothness of Σ was later obtained by C. Herz [2].

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