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Journal of the American Mathematical Society, ISSN 0894-0347, 07/2013, Volume 26, Issue 3, pp. 831 - 852
In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the... 
Minkowski problem | Cone-volume measure | Log-Minkowski problem | Lp-Minkowski problem | L-0-MINKOWSKI PROBLEM | log-Minkowski problem | SURFACE MEASURE | P SOBOLEV INEQUALITIES | POLYTOPES | AFFINE ISOPERIMETRIC-INEQUALITIES | MATHEMATICS | L-p-Minkowski problem | CONVEX HYPERSURFACES | CURVATURE | BODIES | EQUATION | GEOMETRY
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 10, pp. 1857 - 1872
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 05/2012, Volume 262, Issue 9, pp. 4181 - 4204
We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy... 
Logarithmic Sobolev inequality | Affine isoperimetric inequality | MATHEMATICS | Equality
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 07/2016, Volume 271, Issue 2, pp. 454 - 473
We show that the Lp Busemann–Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo... 
Affine Sobolev inequalities | [formula omitted] Busemann–Petty centroid inequality | Affine logarithmic inequalities | Busemann-Petty centroid inequality
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2014, Volume 262, pp. 909 - 931
The logarithmic Minkowski problem asks for necessary and sufficient conditions for a finite Borel measure on the unit sphere so that it is the cone-volume measure of a convex body... 
Polytope | [formula omitted] Minkowski problem | Minkowski problem | Cone-volume measure | Monge–Ampère equation | Logarithmic Minkowski problem | Monge-ampère equation | Logarithmic minkowski problem | L-0-MINKOWSKI PROBLEM | MATHEMATICS | REGULARITY | CONVEX HYPERSURFACES | MEAN-CURVATURE | P SOBOLEV INEQUALITIES | BODIES | EQUATION | AFFINE ISOPERIMETRIC-INEQUALITIES | FLOW | GEOMETRY
Journal Article
JOURNAL OF FUNCTIONAL ANALYSIS, ISSN 0022-1236, 07/2016, Volume 271, Issue 2, pp. 454 - 473
We show that the L-p Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev... 
MATHEMATICS | Affine Sobolev inequalities | L-p Busemann-Petty centroid inequality | HYPERCONTRACTIVITY | HAMILTON-JACOBI EQUATIONS | Affine logarithmic inequalities | ISOPERIMETRIC-INEQUALITIES
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 02/2016, Volume 73, pp. 43 - 58
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 12/2018, Volume 197, Issue 1, pp. 33 - 48
The logarithmic John ellipsoid of a convex body in with its centroid at the origin is introduced by solving a pair of dual optimization problems... 
John ellipsoid | Volume-ratio inequality | MATHEMATICS | POSITIONS | EXTREMAL PROBLEMS | SURFACE-AREA | MINKOWSKI-FIREY THEORY | VOLUME | AFFINE | L-p John ellipsoid
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2015, Volume 427, Issue 2, pp. 905 - 929
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2017, Volume 69, Issue 4, pp. 1565 - 1581
We reduce Iitaka's subadditivity conjecture for the logarithmic Kodaira dimension to a special case of the generalized abundance conjecture by establishing an Iitaka type inequality for Nakayama's... 
Affine varieties | ω-sheaf | Abundance conjecture | Iitaka conjecture | Minimal model program | Nakayama's numerical Kodaira dimension | Logarithmic Kodaira dimension | MATHEMATICS | logarithmic Kodaira dimension | abundance conjecture | affine varieties | (omega)over-cap-sheaf | MINIMAL MODELS | omega-sheaf | minimal model program
Journal Article
Advances in Mathematics, ISSN 0001-8708, 10/2016, Volume 302, pp. 1080 - 1110
.... Our approach is based on the general Lp Busemann–Petty centroid inequality and does not rely on the general Lp Petty projection inequality or the solution of the Lp Minkowski problem. A Brothers... 
Busemann–Petty centroid inequality | Affine Sobolev-type inequalities | Affine Pólya–Szegö principle | Stability estimates | REARRANGEMENT | MATHEMATICS | Busemann-Petty centroid inequality | SHARP SOBOLEV | CONVEX SYMMETRIZATION | Affine Polya-Szego principle | Equality
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 05/2020, Volume 545, p. 123270
.... We comment on the extremizing probability distributions of this LYZ functional, its relation to the escort distributions, a generalized Fisher information and the corresponding Cramér–Rao inequality. We point out potential physical implications of the LYZ entropic functional and of its extremal distributions. 
Nonextensive thermostatistics | Nonadditive entropy | Tsallis entropy | [formula omitted]-entropy | Complexity | FOKKER-PLANCK EQUATION | PHYSICS, MULTIDISCIPLINARY | INEQUALITY | SOBOLEV | MINKOWSKI-FIREY THEORY | IRREVERSIBILITY | GENERALIZED ENTROPIES | q-entropy | AFFINE | H-THEOREM | CRAMER-RAO
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 9
...}$-mixed volume and the Lp $L_{p}$-dual mixed volume. In this article, associated with the (p,q) $(p,q)$-mixed volumes, we establish related cyclic inequalities, monotonic inequalities, and product inequalities. 
52A20 | Cyclic inequality | 52A40 | ( p , q ) $(p,q)$ -mixed volume | Analysis | Monotonic inequality | 52A39 | Mathematics, general | Mathematics | Applications of Mathematics | Product inequality | (p, q) -mixed volume | MATHEMATICS | MATHEMATICS, APPLIED | AFFINE SURFACE-AREA | (p, q)-mixed volume | MINKOWSKI-FIREY THEORY | MIXED VOLUMES | Inequalities | Cases (containers)
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2019, Volume 2019, Issue 1, pp. 1 - 21
Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies... 
mixed quermassintegral | Dual log-Minkowski inequality | Log-Minkowski inequality | dual mixed quermassintegral | mixed affine isoperimetric inequality | Differential geometry | Inequalities | Inequality
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/2019, Volume 371, Issue 2, pp. 971 - 1002
.... When the logarithmic Kodaira dimension \bar {\kappa } is -\infty , we completely characterize the potential density of integral points in terms of the number of irreducible... 
MATHEMATICS | COMPLEMENT | SUBVARIETIES | DIOPHANTINE APPROXIMATION | CURVE | VARIETIES | AFFINE | LOGARITHMIC KODAIRA DIMENSION
Journal Article
by Ma, Lei and Ma, Lei
Geometriae Dedicata, ISSN 0046-5755, 8/2015, Volume 177, Issue 1, pp. 75 - 82
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 9/2012, Volume 48, Issue 2, pp. 281 - 297
Journal Article
Journal of Inequalities and Applications, 12/2019, Volume 2019, Issue 1, pp. 1 - 21
Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies... 
52A20 | L p $L_{p}$ -dual mixed quermassintegral | L p $L_{p}$ -mixed affine isoperimetric inequality | 52A40 | Dual log-Minkowski inequality | Log-Minkowski inequality | Analysis | Mathematics, general | Mathematics | L p $L_{p}$ -mixed quermassintegral | Applications of Mathematics
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2007, Volume 17, Issue 1, pp. 119 - 146
...SIAM J. OPTIM. c Vol. 17, No. 1, pp. 119146 CONSTRAINT REDUCTION FOR LINEAR PROGRAMS WITH MANY INEQUALITY CONSTRAINTS ANDR L. TITS, P.-A. ABSIL, AND WILLIAM P... 
Linear programming | Column generation | Constraint reduction | Mehrotra's predictor-corrector | Affine scaling | Primal-dual interior-point methods | MATHEMATICS, APPLIED | COMPLEXITY ANALYSIS | primal-dual interior-point methods | ALGORITHM | column generation | linear programming | affine scaling | constraint reduction
Journal Article
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