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pro vyhledávání: '"35k96"'
This article introduces the $L_p$-Gauss dual curvature measure and proposes its related $L_p$-Gauss dual Minkowski problem as: for $p,q\in\mathbb{R}$, under what necessary and/or sufficient condition on a non-zero finite Borel measure $\mu$ on unit s
Externí odkaz:
http://arxiv.org/abs/2412.13557
Autor:
Zhao, Xia, Zhao, Peibiao
The Minkowski problem for torsional rigidity ($2$-torsional rigidity) was firstly studied by Colesanti and Fimiani \cite{CA} using variational method. Moreover, Hu \cite{HJ00} also studied this problem by the method of curvature flows and obtained th
Externí odkaz:
http://arxiv.org/abs/2411.00779
We study the regularity of the $p$-Gauss curvature flow with flat side. In our previous paper(arxiv:2403.12292), we obtained the regularity of the interface, namely the boundary of the flat part. In this paper, we study the regularity of the convex h
Externí odkaz:
http://arxiv.org/abs/2407.05663
Autor:
Mei, Xinqun, Weng, Liangjun
In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an isoperimetric type problem in hyperbolic space. By constructing a new
Externí odkaz:
http://arxiv.org/abs/2406.07304
Autor:
Zhao, Xia, Zhao, Peibiao
Recently, Huang and Qin \cite{HY01} introduced the Gaussian chord measure and $L_p$-Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem for $p=1$ and used variational methods to obtain an origin-symme
Externí odkaz:
http://arxiv.org/abs/2406.05635
Autor:
Tosatti, Valentino
We survey some recent developments on solutions of the K\"ahler-Ricci flow on compact K\"ahler manifolds which exist for all positive times.
Comment: 18 pages; submitted to the AMS Contemporary Mathematics volume in memory of Steve Zelditch; fin
Comment: 18 pages; submitted to the AMS Contemporary Mathematics volume in memory of Steve Zelditch; fin
Externí odkaz:
http://arxiv.org/abs/2405.04444
We consider the K\"ahler-Ricci flow on compact K\"ahler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth top
Externí odkaz:
http://arxiv.org/abs/2405.04208
Autor:
Zhao, Xia, Zhao, Peibiao
The Minkowski problem for torsional rigidity ($2$-torsional rigidity) was firstly studied by Colesanti and Fimiani \cite{CA} using variational method. Moreover, Hu, Liu and Ma \cite{HJ00} also studied this problem by method of curvature flows and obt
Externí odkaz:
http://arxiv.org/abs/2404.19266
The Minkowski problem of harmonic measures was first studied by Jerison [19]. Recently, Akman and Mukherjee [1] studied the Minkowski problem corresponding to $p$-harmonic measures on convex domains and generalized Jerison's results. In this paper, w
Externí odkaz:
http://arxiv.org/abs/2404.18757
Autor:
Zhou, Yang, Zhu, Ruixuan
We prove the existence and regularity of convex solutions to the first initial-boundary value problem of the parabolic Monge-Amp\`ere equation $$ \left\{\begin{eqnarray} &u_t=\det D^2u\quad\text{ in } Q_T, \\ &u=\phi\quad\text{ on }\partial_pQ_T, \en
Externí odkaz:
http://arxiv.org/abs/2403.11479