1988, A series of comprehensive studies in mathematics, ISBN 3540136150, Volume 285., xiv, 331

Book

1961, School ed., New mathematical library, Volume 4, 132

Book

2001, Cambridge tracts in mathematics, ISBN 0521802679, Volume 145., xii, 268

Book

1980, ISBN 0273084232, Volume 7., x, 228

Book

Journal of Functional Analysis, ISSN 0022-1236, 08/2009, Volume 257, Issue 3, pp. 641 - 658

A new sharp affine L Sobolev inequality for functions on R is established. This inequality strengthens and implies the previously known affine L Sobolev...

Sobolev inequalities | Affine isoperimetric inequalities

Sobolev inequalities | Affine isoperimetric inequalities

Journal Article

1951, Annals of mathematics studies, Volume no. 27., xvi, 279

Book

BERNOULLI, ISSN 1350-7265, 11/2019, Volume 25, Issue 4B, pp. 3978 - 4006

We investigate links between the so-called Stein's density approach in dimension one and some functional and concentration inequalities. We show that measures...

weighted Poincare inequality | weighted log-Sobolev inequality | concentration inequality | tail bound | SIZE BIASED COUPLINGS | STATISTICS & PROBABILITY | SPECTRAL GAP | Stein kernel | isoperimetric constant | SOBOLEV INEQUALITIES | covariance identity

weighted Poincare inequality | weighted log-Sobolev inequality | concentration inequality | tail bound | SIZE BIASED COUPLINGS | STATISTICS & PROBABILITY | SPECTRAL GAP | Stein kernel | isoperimetric constant | SOBOLEV INEQUALITIES | covariance identity

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2009, Volume 257, Issue 3, pp. 641 - 658

A new sharp affine Sobolev inequality for functions on is established. This inequality strengthens and implies the previously known affine Sobolev inequality...

Sobolev inequalities | Affine isoperimetric inequalities | MATHEMATICS | SHARP SOBOLEV | MINKOWSKI-FIREY THEORY | VALUATIONS | BODIES | ISOPERIMETRIC-INEQUALITIES

Sobolev inequalities | Affine isoperimetric inequalities | MATHEMATICS | SHARP SOBOLEV | MINKOWSKI-FIREY THEORY | VALUATIONS | BODIES | ISOPERIMETRIC-INEQUALITIES

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...

MATHEMATICS | Affine Sobolev inequalities | L-p Busemann-Petty centroid inequality | HYPERCONTRACTIVITY | HAMILTON-JACOBI EQUATIONS | Affine logarithmic inequalities | ISOPERIMETRIC-INEQUALITIES

MATHEMATICS | Affine Sobolev inequalities | L-p Busemann-Petty centroid inequality | HYPERCONTRACTIVITY | HAMILTON-JACOBI EQUATIONS | Affine logarithmic inequalities | ISOPERIMETRIC-INEQUALITIES

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2015, Volume 427, Issue 2, pp. 905 - 929

The Orlicz–Brunn–Minkowski theory received considerable attention recently, and many results in the -Brunn–Minkowski theory have been extended to their Orlicz...

Orlicz–Brunn–Minkowski theory | Geominimal surface area | The Blaschke–Santaló inequality | Affine surface area | Affine isoperimetric inequalities | The inverse Santaló inequality | Orlicz-Brunn-Minkowski theory | The Blaschke-Santaló inequality | MATHEMATICS, APPLIED | The inverse Santalo inequality | SURFACE-AREA | PROOF | INVARIANT VALUATIONS | The Blaschke-Santalo inequality | MATHEMATICS | MINKOWSKI-FIREY THEORY | BODIES

Orlicz–Brunn–Minkowski theory | Geominimal surface area | The Blaschke–Santaló inequality | Affine surface area | Affine isoperimetric inequalities | The inverse Santaló inequality | Orlicz-Brunn-Minkowski theory | The Blaschke-Santaló inequality | MATHEMATICS, APPLIED | The inverse Santalo inequality | SURFACE-AREA | PROOF | INVARIANT VALUATIONS | The Blaschke-Santalo inequality | MATHEMATICS | MINKOWSKI-FIREY THEORY | BODIES

Journal Article

1997, Memoirs of the American Mathematical Society, ISBN 0821806424, Volume no. 616., viii, 111

Book

Advances in Mathematics, ISSN 0001-8708, 11/2019, Volume 356, p. 106811

It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly...

Sobolev inequality | Valuation | Isoperimetric inequality | MATHEMATICS | POLYA-SZEGO PRINCIPLE | PROJECTION BODIES | MINKOWSKI-FIREY THEORY | INVARIANT VALUATIONS | ENDOMORPHISMS | SOBOLEV

Sobolev inequality | Valuation | Isoperimetric inequality | MATHEMATICS | POLYA-SZEGO PRINCIPLE | PROJECTION BODIES | MINKOWSKI-FIREY THEORY | INVARIANT VALUATIONS | ENDOMORPHISMS | SOBOLEV

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2012, Volume 231, Issue 3-4, pp. 1974 - 1997

For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each...

Minkowski–Firey [formula omitted]-combinations | Brunn–Minkowski–Firey inequality | Minkowski mixed-volume inequality | Brunn–Minkowski inequality | Brunn-Minkowski-Firey inequality | combinations | Brunn-Minkowski inequality | Minkowski-Firey L | L-0-MINKOWSKI PROBLEM | VOLUME INEQUALITIES | ISOTROPIC MEASURES | Minkowski-Firey L-p-combinations | VALUED VALUATIONS | CONVEX-BODIES | SURFACE-AREAS | P SOBOLEV INEQUALITIES | CENTROID BODIES | AFFINE ISOPERIMETRIC-INEQUALITIES | MATHEMATICS | INTERSECTION BODIES | Equality

Minkowski–Firey [formula omitted]-combinations | Brunn–Minkowski–Firey inequality | Minkowski mixed-volume inequality | Brunn–Minkowski inequality | Brunn-Minkowski-Firey inequality | combinations | Brunn-Minkowski inequality | Minkowski-Firey L | L-0-MINKOWSKI PROBLEM | VOLUME INEQUALITIES | ISOTROPIC MEASURES | Minkowski-Firey L-p-combinations | VALUED VALUATIONS | CONVEX-BODIES | SURFACE-AREAS | P SOBOLEV INEQUALITIES | CENTROID BODIES | AFFINE ISOPERIMETRIC-INEQUALITIES | MATHEMATICS | INTERSECTION BODIES | Equality

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2019, Volume 372, Issue 4, pp. 2753 - 2776

We establish sharp affine weighted L^p Sobolev type inequalities by using the L_p Busemann-Petty centroid inequality proved by Lutwak, Yang, and Zhang. Our...

MATHEMATICS | centroid bodies | Sobolev inequality | convex body | ISOPERIMETRIC-INEQUALITIES | MINKOWSKI

MATHEMATICS | centroid bodies | Sobolev inequality | convex body | ISOPERIMETRIC-INEQUALITIES | MINKOWSKI

Journal Article

15.
Full Text
Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3, p. 1

We provide a sharp quantitative version of the Gaussian concentration inequality: for every r > 0, the difference between the measure of the r-enlargement of a...

60E15 | 49Q20 | 52A40 | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | Equality

60E15 | 49Q20 | 52A40 | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | Equality

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 3522 - 3552

Extremal functions are exhibited in Poincare trace inequalities for functions of bounded variation in the unit ball Bn of the n-dimensional Euclidean spaceRn....

Isoperimetric inequalities | Functions of bounded variation | Sobolev spaces | Boundary traces | Poincaré inequalities | Sharp constants | ISOPERIMETRIC INEQUALITY | CONSTANT | SOBOLEV INEQUALITIES | MATHEMATICS | BALLS | WORST | EXTREMAL-FUNCTIONS | Poincare inequalities

Isoperimetric inequalities | Functions of bounded variation | Sobolev spaces | Boundary traces | Poincaré inequalities | Sharp constants | ISOPERIMETRIC INEQUALITY | CONSTANT | SOBOLEV INEQUALITIES | MATHEMATICS | BALLS | WORST | EXTREMAL-FUNCTIONS | Poincare inequalities

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 04/2019, Volume 199, Issue 1, pp. 335 - 353

By proving a "weighted" reverse affine isoperimetric inequality and its dual, we establish a sharp L.sub.[infinity] L [infinity] Loomis--Whitney inequality and...

Reverse affine isoperimetric inequality | Loomis–Whitney inequality | Isotropic measure | Weighted ℓ | balls | zonoid

Reverse affine isoperimetric inequality | Loomis–Whitney inequality | Isotropic measure | Weighted ℓ | balls | zonoid

Journal Article

Advances in Mathematics, ISSN 0001-8708, 02/2018, Volume 325, pp. 824 - 863

Given one metric measure space satisfying a linear Brunn–Minkowski inequality, and a second one satisfying a Brunn–Minkowski inequality with exponent , we...

Gaussian measure | Isoperimetric inequality | Metric measure space | Product space | Product measure | Brunn–Minkowski inequality | MATHEMATICS | Brunn-Minkowski inequality

Gaussian measure | Isoperimetric inequality | Metric measure space | Product space | Product measure | Brunn–Minkowski inequality | MATHEMATICS | Brunn-Minkowski inequality

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 2, pp. 1676 - 1689

In this paper we prove that the disc is a maximiser of the Schatten -norm of the logarithmic potential operator among all domains of a given measure in , for...

Pólya inequality | Characteristic numbers | Rayleigh–Faber–Krahn inequality | Isoperimetric inequality | Logarithmic potential | Schatten class | Rayleigh-Faber-Krahn inequality | LAPLACIAN | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | Polya inequality | Mathematics - Functional Analysis

Pólya inequality | Characteristic numbers | Rayleigh–Faber–Krahn inequality | Isoperimetric inequality | Logarithmic potential | Schatten class | Rayleigh-Faber-Krahn inequality | LAPLACIAN | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | Polya inequality | Mathematics - Functional Analysis

Journal Article

2011, Volume 545

Conference Proceeding

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