Local LP-Brunn-Minkowski inequalities for p<1 / Alexander V. Kolesnikov, Emanuel Milman.

Format:

Book

Author/Creator:

Kolesnikov, Alexander V., author.

Milman, Emanuel, 1977- author.

Series:

Memoirs of the American Mathematical Society ; no. 1360.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 1360

Language:

English

Subjects (All):

Convex domains.

Mathematical analysis.

Minkowski geometry.

Inequalities (Mathematics).

Physical Description:

v, 78 pages ; 26 cm.

Place of Publication:

Providence, RI : AMS, American Mathematical Society, [2022]

Contents:

Chapter 1. Introduction

1.1 Previously known partial results

1.2 Main results

1.3 Spectral interpretation vs the Hilbert-Brunn-Minkowski operator

1.4 Method of proof

1.5 Applications

Chapter 2. Notation

Chapter 3. Global vs. local formulations of the LP-Brunn-Minkowski conjecture

3.1 Standard equivalent global formulations 3.2 global vs. local LP-Brunn-Minkowski

Chapter 4. Local LP-Brunn-Minkowski conjecture - infinitesimal formulation

4.1 Mixed surface area and volume of C2 functions

4.2 Properties of mixed surface area and volume

4.3 Second LP-Minkowski inequality

4.4 Comparison with classical p=1 case

4.5 Infinitesimal formulation on Sn-1

4.6 Infinitesimal formulation On ∂K

Chapter 5. Relation to Hilbert-Brunn-Minkowski operator and linear equivariance

5.1 Hilbert-Brunn-Minkowski operator

5.2 Linear equivariance of the Hilbert-Brunn-Minkowski operator

5.3 Spectral minimization problem and potential extremizers

Chapter 6. Obtaining estimates via the Reilly formula

6.1 A sufficient condition for confirming the local p-BM inequality

6.2 General estimate on D(K)

6.3 Examples

Chapter 7. The second Steklov operator and BH (Bn2)

7.1 Second Steklov operator

7.2 Computing BH (Bn2)

Chapter 8. Unconditional convex bodies and the cube

8.1 Unconditional convex bodies

8.2 The cube

Chapter 9. Local log-Brunn-Minkowski via the Reilly Formula

9.1 Sufficient condition for verifying local log-Brunn-Minkowski

9.2 An alternative derivation via estimating BH(K)

Chapter 10. Continuity of BH, B, D with application to Bnq

10.1 Continuity of BH, B, D in C-topology

10.2 The cube

10.3 Unit-balls of lnq

Chapter 11. Local uniqueness for even Lp-Minkowski problem

Chapter 12. Stability estimates for Brunn-Minkowski and isoperimetric inequalities

12.1 New stability estimates for origin-symmetric convex bodies with respect to variance

12.2 Improved stability estimates for all convex bodies with respect to asymmetry

Bibliography

Notes:

"May 2022, volume 277, number 1360 (first of 6 numbers)."

Includes bibliographical references (pages 75-78).

ISBN:

1470451603

9781470451608

OCLC:

1314258841