A sharp centro-affine isospectral inequality of Szegö-Weinberger type and the $L^p$-Minkowski problem

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Inequalities and extremum problems involving convexity in convex geometry (52A40)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Mirror symmetric solutions to the centro-affine Minkowski problem
Dar's conjecture and the log-Brunn-Minkowski inequality
Multiple solutions of the $L_{p}$-Minkowski problem
The log-Brunn-Minkowski inequality
The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
Cone-volume measure of general centered convex bodies
Interior $W^{2,p}$ estimates for solutions of the Monge-Ampère equation
A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
Deforming convex hypersurfaces by the $n$th root of the Gaussian curvature
Representation of $L_ p$-norms and isometric embedding in $L_ p$- spaces
Evolving convex curves
Evolving plane curves by curvature in relative geometries
Complete noncompact self-similar solutions of Gauss curvature flows. I: Positive powers
On the number of solutions to the discrete two-dimensional $L_{0}$-Minkowski problem.
Complete noncompact self-similar solutions of Gauss curvature flows. II. Negative powers
A new ellipsoid associated with convex bodies
Motion of hypersurfaces by Gauss curvature
The discrete planar $L_0$-Minkowski problem
$L_ p$ affine isoperimetric inequalities.
The logarithmic John ellipsoid
The $L_{p}$-Minkowski problem for $-n < p < 1$
Asymptotic behavior of flows by powers of the Gaussian curvature
Characteristic properties of ellipsoids and convex quadrics
Sharp affine $L_ p$ Sobolev inequalities.
Gauss curvature flow: The fate of the rolling stones
New volume ratio properties for convex symmetric bodies in ${\mathbb{R}}^ n$
On the regularity of solutions to a generalization of the Minkowski problem
Isoperimetric problems for convex bodies and a localization lemma
The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
On the regularity of the $L_p$ Minkowski problem
Rotationally symmetric solutions to the $L_p$-Minkowski problem
Brascamp-Lieb-type inequalities on weighted Riemannian manifolds with boundary
On the $L_{p}$ Monge-Ampère equation
An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture
On the $L_p$-Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures
Bourgain's slicing problem and KLS isoperimetry up to polylog
The extremals of Minkowski's quadratic inequality
The $L_p$-Brunn-Minkowski inequality for $p<1$
The logarithmic Minkowski problem for polytopes
Smoothness in the $L_p$ Minkowski problem for $p<1$
The $L_p$ Minkowski problem for polytopes for $0 < p < 1$
Nonuniqueness of solutions to the $L_p$-Minkowski problem
On the stability of Brunn-Minkowski type inequalities
The necessary condition for the discrete $L_{0}$-Minkowski problem in ${\mathbb{R}}^{2}$
On the $L_{p}$ Minkowski problem for polytopes
The $L_p$-Minkowski problem and the Minkowski problem in centroaffine geometry
The centro-affine Minkowski problem for polytopes
A new proof of the log-Brunn-Minkowski inequality
Remarks on the conjectured log-Brunn-Minkowski inequality
Flow by powers of the Gauss curvature
Equivalence of the local and global versions of the $L^p$-Brunn-Minkowski inequality
On the Discrete Logarithmic Minkowski Problem
MORE ON LOGARITHMIC SUMS OF CONVEX BODIES
Continuity of the solution to the $L_{p}$ Minkowski problem
Approximately gaussian marginals and the hyperplane conjecture
Mahler's Conjecture and Curvature
Shapes of worn stones
On the regularity of the solution of then-dimensional Minkowski problem
Convex Bodies with Identical John and LYZ Ellipsoids
The logarithmic Minkowski problem for non-symmetric measures
$L_p$ John Ellipsoids
Classification of limiting shapes for isotropic curve flows
A geometric inequality and a low 𝑀-estimate
On the $L_{p}$-Minkowski problem
Fourier transform and Firey projections of convex bodies
Entropy jumps for isotropic log-concave random vectors and spectral gap
The logarithmic Minkowski problem
Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds
On the Local Version of the Log-Brunn–Minkowski Conjecture and Some New Related Geometric Inequalities
Nonuniqueness of Solutions to the Lp Dual Minkowski Problem
Log-Brunn-Minkowski inequality under symmetry
Mass transportation functionals on the sphere with applications to the logarithmic Minkowski problem
Infinitely Many Solutions for Centro-affine Minkowski Problem
The Lp Minkowski problem for polytopes for p<0
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
Convex Bodies The Brunn-MinkowskiTheory
$p$-Means of Convex Bodies.
On Differential Geometry in the Large, I (Minkowski's Problem)
The Weyl and Minkowski problems in differential geometry in the large
Sur une nouvelle classe de surfaces.

A sharp centro-affine isospectral inequality of Szegö-Weinberger type and the \(L^p\)-Minkowski problem