Zobrazeno 1 - 10
of 168
pro vyhledávání: '"Karoly, J"'
For fixed positive integer $n$, $p\in[0,1]$, $a\in(0,1)$, we prove that if a function $g:\mathbb{S}^{n-1}\to \mathbb{R}$ is sufficiently close to 1, in the $C^a$ sense, then there exists a unique convex body $K$ whose $L_p$ curvature function equals
Externí odkaz:
http://arxiv.org/abs/2308.03367
Autor:
Böröczky, Károly J., Guan, Pengfei
We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak's $L^p$-Minkowski problem on $S^n$ which were obtained by other methods.
Externí odkaz:
http://arxiv.org/abs/2307.12107
Autor:
Bonne, L., Andersson, B-G, Minchin, R., Soam, A., Yaldaei, J., Kulas, K., Karoly, J., Knee, L. B. G., Kumar, S., Roy, N.
Photodissociation regions (PDRs), where the (far-)ultraviolet light from hot young stars interact with the gas in surrounding molecular clouds, provide laboratories for understanding the nature and role of feedback by star formation on the interstell
Externí odkaz:
http://arxiv.org/abs/2304.13669
Hyperbolic width functions and characterizations of bodies of constant width in the hyperbolic space
We discuss basic properties of several different width functions in the $n$-dimensional hyperbolic space such as continuity, and we also define a new hyperbolic width as the extension of Leichtweiss' width function. Then we prove a characterization t
Externí odkaz:
http://arxiv.org/abs/2303.16814
We prove explicit stability estimates for the sphere packing problem in dimensions 8 and 24, showing that, in the lattice case, if a lattice is $\sim \varepsilon$ close to satisfying the optimal density, then it is, in a suitable sense, $O(\varepsilo
Externí odkaz:
http://arxiv.org/abs/2303.07908
Autor:
Boroczky, Karoly J.
The current state of art concerning the $L_p$ Minkowski problem as a Monge-Ampere equation on the sphere and Lutwak's Logarithmic Minkowski conjecture about the uniqueness of even solution in the $p=0$ case are surveyed and connections to many relate
Externí odkaz:
http://arxiv.org/abs/2210.00194
Autor:
Böröczky, Károly J., Sagmeister, Ádám
We prove a stability version of the isodiametric inequality on the sphere and in the hyperbolic space.
Externí odkaz:
http://arxiv.org/abs/2207.03043
Autor:
Boroczky, Karoly J., Sagmeister, Adam
Extending Blaschke and Lebesgue's classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have the minimal area among convex domains of constant width $D$. We prove
Externí odkaz:
http://arxiv.org/abs/2203.16636
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe's reverse Brascamp-Lieb inequality.
Externí odkaz:
http://arxiv.org/abs/2203.01428
We prove that if a triplet of functions satisfies almost equality in the Pr\'ekopa-Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable funct
Externí odkaz:
http://arxiv.org/abs/2201.11564