Chord measures in integral geometry and their Minkowski problems

Cites Work

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Dar's conjecture and the log-Brunn-Minkowski inequality
Rényi divergence and \(L_p\)-affine surface area for convex bodies
The log-Brunn-Minkowski inequality
The dual Minkowski problem for negative indices
\(\mathrm{SL}(n)\) invariant valuations on polytopes
Minkowski areas and valuations
Extremum problems for the cone volume functional of convex polytopes
Hermitian integral geometry
The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
Minkowski valuations intertwining the special linear group
Cone-volume measure and stability
Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
Projection problems for symmetric polytopes
Cone-volume measure of general centered convex bodies
Inequalities for mixed \(p\)-affine surface area
General \(L_{p}\) affine isoperimetric inequalities
Affine Moser-Trudinger and Morrey-Sobolev inequalities
Intersection bodies and dual mixed volumes
On the Busemann-Petty problem for perturbations of the ball
Curvature measures of convex bodies
A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\)
An analytic solution to the Busemann-Petty problem on sections of convex bodies
The isoperimetric theorem for general integrands
A Minkowski problem for electrostatic capacity
The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
Ellipsoids and matrix-valued valuations
On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
On the \(p\)-affine surface area
A new ellipsoid associated with convex bodies
The discrete planar \(L_0\)-Minkowski problem
The affine Sobolev inequality.
\(L_ p\) affine isoperimetric inequalities.
Existence of solutions to the even dual Minkowski problem
General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
On the \(L_p\) dual Minkowski problem
Subspace concentration of dual curvature measures of symmetric convex bodies
Minkowski valuations and generalized valuations
Necessary subspace concentration conditions for the even dual Minkowski problem
Minkowski valuations on lattice polytopes
Sharp affine \(L_ p\) Sobolev inequalities.
Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
Gauss curvature flow: The fate of the rolling stones
A positive answer to the Busemann-Petty problem in three dimensions
The Cramer-Rao inequality for star bodies
Projecting the surface measure of the sphere of \({\ell}_p^n\)
Surface bodies and \(p\)-affine surface area
The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
Curvature relations and affine surface area for a general convex body and its polar
Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
The \(L_p\)-Brunn-Minkowski inequality for \(p<1\)
The \(L_p\) Minkowski problem for the electrostatic \(\mathfrak{p}\)-capacity
The logarithmic Minkowski problem for polytopes
Dual mixed volumes
General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II
Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
The dual Minkowski problem for symmetric convex bodies
Asymmetric affine \(L_p\) Sobolev inequalities
Smooth solutions to the \(L_p\) dual Minkowski problem
Cone-volume measures of polytopes
Integral geometry of complex space forms
Valuations and surface area measures
Theory of valuations on manifolds: A survey
On the \(L_{p}\) Minkowski problem for polytopes
The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
Remarks on the conjectured log-Brunn-Minkowski inequality
On \(L_{p}\)-affine surface area and curvature measures
Relative entropy of cone measures and L _p centroid bodies
The Centro-Affine Hadwiger Theorem
Curvature Measures
Ehrhart Polynomials and Successive Minima
Intersection bodies and valuations
The surface measure and cone measure on the sphere of ℓ_{𝑝}ⁿ
Stochastic and Integral Geometry
Intersection bodies, positive definite distributions, and the Busemann-Petty problem
Dual kinematic formulas
Affine inequalities and radial mean bodies
The logarithmic Minkowski problem for non-symmetric measures
Classification of limiting shapes for isotropic curve flows
The logarithmic Minkowski problem
On the Local Version of the Log-Brunn–Minkowski Conjecture and Some New Related Geometric Inequalities
Stability of Tangent Bundles on Smooth Toric Picard-rank-2 Varieties and Surfaces
Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1
Convex Bodies The Brunn-MinkowskiTheory
Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
A functional analytic approach to intersection bodies