Explore a mathematical lecture addressing solutions to the 5th and 8th Busemann-Petty problems for bodies close to the Euclidean ball in Banach-Mazur distance. Delve into key concepts including curvature functions, Radon transforms, and spherical harmonic expansions. Follow the speaker's journey through problem definitions, geometric interpretations, and known results, culminating in a detailed proof and summary of the solution. Gain insights into this collaborative work with M. Angeles Alfonseca, Fedor Nazarov, and Dmitry Ryabogin, presented at the Hausdorff Center for Mathematics.
Vlad Yaskin- A Solution to the 5th and 8th Busemann-Petty Problems Near the Euclidean Ball
Hausdorff Center for Mathematics via YouTube
Overview
Syllabus
Intro
BusemannPetty problems
Basic definitions
Curvature function
Problem number 5
Problem number 8
Observations on condition 1
Geometric interpretation of problem 5
What is known about these problems
Examples
Proof
Observations
Radon transform
Condition
Radium transform
Second order harmonics
Small harmonics
Spherical harmonic expansion
The head and tail
The 8th problem
A simpler equation
A contraction
Summary
Solution
Taught by
Hausdorff Center for Mathematics
