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Author:
Kolesnikov, Alexander V., author
Title:
Local LP-Brunn-Minkowski inequalities for p<1 / Alexander V. Kolesnikov, Emanuel Milman.
Publisher:
AMSAmerican Mathematical Society,
Copyright Date:
2022
Description:
v, 78 pages ; 26 cm.
Subject:
Convex domains.
Mathematical analysis.
Minkowski geometry.
Inequalities (Mathematics)
Other Authors:
Milman, Emanuel, 1977- author.
Notes:
"May 2022, volume 277, number 1360 (first of 6 numbers)." Includes bibliographical references (pages 75-78).
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.
Series:
Memoirs of the American Mathematical Society, 0065-9266 ; Number 1360
ISBN:
9781470451608
1470451603
OCLC:
(OCoLC)1314258841
Locations:
OVUX522 -- University of Iowa Libraries (Iowa City)

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