Analysis and geometry near the unit ball: proofs, counterexamples, and open questions
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M. Angeles Alfonseca
Abstract
We present several theorems, counterexamples, and open questions related to convex bodies close to the unit ball. The techniques include spherical harmonic decomposition and some elements of perturbation theory. We hope that this short survey will attract the attention of both young and mature researchers who will be able to surpass our results and resolve some questions we left unanswered.
Abstract
We present several theorems, counterexamples, and open questions related to convex bodies close to the unit ball. The techniques include spherical harmonic decomposition and some elements of perturbation theory. We hope that this short survey will attract the attention of both young and mature researchers who will be able to surpass our results and resolve some questions we left unanswered.
Chapters in this book
- Frontmatter I
- Contents V
- Algebraically integrable bodies and related properties of the Radon transform 1
- The covariogram problem 37
- The logarithmic Minkowski conjecture and the Lp-Minkowski problem 83
- Bellman functions and continuous time 119
- Volume product 163
- Inequalities for sections and projections of convex bodies 223
- Borderline estimates for weighted singular operators and concavity 257
- Extremal sections and projections of certain convex bodies: a survey 343
- When does e−/τ/ maximize Fourier extension for a conic section? 391
- Affine surface area 427
- Analysis and geometry near the unit ball: proofs, counterexamples, and open questions 445
- Index 469
Chapters in this book
- Frontmatter I
- Contents V
- Algebraically integrable bodies and related properties of the Radon transform 1
- The covariogram problem 37
- The logarithmic Minkowski conjecture and the Lp-Minkowski problem 83
- Bellman functions and continuous time 119
- Volume product 163
- Inequalities for sections and projections of convex bodies 223
- Borderline estimates for weighted singular operators and concavity 257
- Extremal sections and projections of certain convex bodies: a survey 343
- When does e−/τ/ maximize Fourier extension for a conic section? 391
- Affine surface area 427
- Analysis and geometry near the unit ball: proofs, counterexamples, and open questions 445
- Index 469
