A5017014622- Point processes and geometric inequalities
- Geometric Analysis and Curvature Flows
- Mathematics and Applications
- Computational Geometry and Mesh Generation
- Mathematical Inequalities and Applications
- Mathematical Approximation and Integration
- Diffusion and Search Dynamics
- Analytic and geometric function theory
- Prion Diseases and Protein Misfolding
- Digital Image Processing Techniques
- Quasicrystal Structures and Properties
- Optimization and Packing Problems
- Mathematical Dynamics and Fractals
- Morphological variations and asymmetry
- Limits and Structures in Graph Theory
- Pharmacological Effects of Medicinal Plants
- Nonlinear Partial Differential Equations
- graph theory and CDMA systems
- Advanced Banach Space Theory
- Advanced Combinatorial Mathematics
- Advanced Numerical Analysis Techniques
- Geometry and complex manifolds
- Functional Equations Stability Results
- Graph theory and applications
- Geometric and Algebraic Topology
Alfréd Rényi Institute of Mathematics
2015-2024
Hungarian Academy of Sciences
2013-2024
Universidad Europea
2024
Eötvös Loránd University
2008-2021
Central European University
2012-2017
Hungarian National Bank
2013
Universitat Politècnica de Catalunya
2010-2012
McMaster University
2009
University of Toronto
2009
University of Fribourg
2004
In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a measure on unit sphere is cone-volume of ball finite-dimensional Banach space.
A new sufficient condition for the existence of a solution logarithmic Minkowski problem is established. This contains one established by Zhu [70] and discrete case Böröczky et al. [7] as two important special cases.
We prove a tight subspace concentration inequality for the dual curvature measures of symmetric convex body.
Necessary and sufficient conditions are given in order for a Borel measure on the Euclidean sphere to have an affine image that is isotropic. A sharp reverse isoperimetric inequality measures presented. This leads inequalities convex bodies.
We verify a conjecture of Lutwak, Yang, and Zhang about the equality case in Orlicz-Petty projection inequality, provide an essentially optimal stability version.
Abstract For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish general framework for showing stability such and use prove two spherical codes formed by minimal vectors lattice $$E_8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> Leech lattice.
The paper focuses on possible hyperbolic versions of the classical Pal isominwidth inequality in R^2 from 1921, which states that for a fixed minimal width, regular triangle has area. We note problem is still wide open R^n n>2. Recent work sphere S^2 shows solution spherical when width at most \pi/2 according to Bezdek and Blekherman, while Freyer Sagmeister proved minimizer polar Reuleaux greater than \pi/2. In this paper, discussed with respect probably natural notion due Lassak space H^n...
We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to n independent hyperplanes, and discuss equality case uniqueness of solution related logarithmic Minkowski problem.We also clarify a small gap in known argument classifying unconditional bodies.
We study the number of facets convex hull n independent standard Gaussian points in d-dimensional Euclidean space. In particular, we are interested expected when dimension is allowed to grow with sample size. establish an explicit asymptotic formula that valid whenever d/n tends zero. also obtain value d close n.
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over integers and are translation invariant. In contravariant case, only such multiples projection bodies. equivariant generalized difference bodies combined with newly defined discrete Steiner point.