Intrinsic and dual volume deviations of convex bodies and polytopes
We establish estimates for the asymptotic best approximation of the Euclidean unit ball by
polytopes under a notion of distance induced by the intrinsic volumes. We also introduce a …
polytopes under a notion of distance induced by the intrinsic volumes. We also introduce a …
The -floating area, curvature entropy, and isoperimetric inequalities on the sphere
F Besau, EM Werner - arXiv preprint arXiv:2411.01631, 2024 - arxiv.org
We explore analogs of classical centro-affine invariant isoperimetric inequalities, such as the
Blaschke--Santal\'o inequality and the $ L_p $-affine isoperimetric inequalities, for convex …
Blaschke--Santal\'o inequality and the $ L_p $-affine isoperimetric inequalities, for convex …
[PDF][PDF] The Isoperimetric inequality, the Brunn-Minkowski theory and Minkowski type Monge-Ampere equations on the sphere
The main topic of the book is how Geometric Isoperimetric-type inequalities intervene with
functional inequalities such as the Prekopa-Leindler inequality, the Sobolev inequality …
functional inequalities such as the Prekopa-Leindler inequality, the Sobolev inequality …
Curvature functionals on convex bodies
We investigate the weighted Brunn–Minkowski theory. We show that they are valuations on
the set of convex bodies and prove isoperimetric inequalities for them. We show that they …
the set of convex bodies and prove isoperimetric inequalities for them. We show that they …
[PDF][PDF] On some problems in Random Matrix Theory and Convex Geometry
K Tatarko - 2020 - era.library.ualberta.ca
This thesis is devoted to several problems in Random Matrix Theory and Convex Geometry.
Its content is based on four papers. In the first part, we establish an upper estimate for the …
Its content is based on four papers. In the first part, we establish an upper estimate for the …