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Akademický článek
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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
In [Calc. Var., 57:5 (2018)], Hong-Ye-Zhang proposed the $p$-capacitary Orlicz-Minkowski problem and proved the existence of convex solutions to this problem by variational method for $p\in(1,n)$. However, the smoothness and uniqueness of solutions a
Externí odkaz:
http://arxiv.org/abs/2305.14830
Autor:
Sheng, Weimin, Xue, Ke
In this paper the Orlicz-Minkowski problem for torsional rigidity, a generalization of the classical Minkowski problem, is studied. Using the flow method, we obtain a new existence result of solutions to this problem for general measures.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/2212.01824
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 10, Iss 1, Pp 330-343 (2022)
Liu and Lu [27] investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions. The present paper investigates a inverse Gauss curvature flow, and achieves the lon
Externí odkaz:
https://doaj.org/article/0b5245a2be974c318e8276bf6ac2f393
Autor:
Liu, YanNan, Lu, Jian
In this paper a generalized Gauss curvature flow about a convex hypersurface in the Euclidean $n$-space is studied. This flow is closely related to the Orlicz-Minkowski problem, which involves Gauss curvature and a function of support function. Under
Externí odkaz:
http://arxiv.org/abs/2005.02376
Autor:
Xing, Sudan, Ye, Deping
Publikováno v:
Indiana University Mathematics Journal, 2020 Jan 01. 69(2), 621-655.
Externí odkaz:
https://www.jstor.org/stable/26959156
In this paper we study the dual Orlicz-Minkowski problem, which is a generalization of the dual Minkowski problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we obt
Externí odkaz:
http://arxiv.org/abs/2005.02639