Results 1 to 10 of about 10 (10)
Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure
Advanced Nonlinear Studies, 2023 In this article, we study the Musielak-Orlicz-Gauss image problem based on the Gauss curvature flow in Li et al. We deal with some cases in which there is no uniform estimate for the Gauss curvature flow.
Li Qi-Rui, Yi Caihong
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Inverse Gauss Curvature Flows and Orlicz Minkowski Problem
Analysis and Geometry in Metric Spaces, 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.
Chen Bin, Cui Jingshi, Zhao Peibiao
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A curvature flow to the Lp Minkowski-type problem of q-capacity
Advanced Nonlinear Studies, 2023 This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
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Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations
Advanced Nonlinear Studies, 2020 In this paper, we study the Cauchy problem of the parabolic Monge–Ampère ...
Dai Limei, Bao Jiguang
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Contact manifolds, Lagrangian Grassmannians and PDEs
Complex Manifolds, 2018 In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1)-dimensional contact manifold and the so-called ...
Eshkobilov Olimjon +3 more
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Advanced Nonlinear StudiesIn the present paper, we first establish and verify a new sharp hyperbolic version of the Michael-Simon inequality for mean curvatures in hyperbolic space Hn+1 ${\mathbb{H}}^{n+1}$ based on the locally constrained inverse curvature flow introduced by ...
Cui Jingshi, Zhao Peibiao
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Collapsing immortal Kähler-Ricci flows
Forum of Mathematics, PiWe consider the Kähler-Ricci flow on compact Kähler 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 topology ...
Hans-Joachim Hein +2 more
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Generalized Gaussian curvature flows related to the Orlicz Gaussian Minkowski problem
Advanced Nonlinear StudiesIn this paper, we investigate two anisotropic Gaussian curvature flows. Through establishing the long-time existence and congergence for these two flows, we derive the existence results for the Orlicz-Gaussian Minkowski problem in both origin-symmetric ...
Liu Yannan, Peng Yuxin
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Advanced Nonlinear StudiesIn this paper, we consider a class of functionals subject to a duality restriction. The functional is of the form J(Ω,Ω*)=∫Ωf+∫Ω*g $\mathcal{J}\left({\Omega},{{\Omega}}^{{\ast}}\right)={\int }_{{\Omega}}f+{\int }_{{{\Omega}}^{{\ast}}}g$ , where f, g are ...
Guang Qiang, Li Qi-Rui, Wang Xu-Jia
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Advances in Nonlinear AnalysisBrendle [Sobolev inequalities in manifolds with nonnegative curvature, Comm. Pure Appl. Math. 76 (2022), no. 9, 2192–2218] successfully establishes the sharp Michael–Simon inequality for mean curvature on Riemannian manifolds with nonnegative sectional ...
Cui Jingshi, Zhao Peibiao
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