Related papers: A flow method for the dual Orlicz-Minkowski proble…
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 $\mu$…
We study long-time existence and asymptotic behaviour for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature…
We study the long-time existence and asymptotic behavior of a class of anisotropic capillary Gauss curvature flows. As an application, we provide a flow approach to the existence of smooth solutions to the capillary even $L_p$ Minkowski…
The variation of a class of Orlicz moments with respect to the Asplund sum within the class of log-concave functions is demonstrated. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave…
General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang. These new measures unify several other geometric measures of the Brunn-Minkowski theory and the dual Brunn-Minkowski theory. $L_p$ dual curvature…
In this paper, we obtain the existence result of smooth solutions to the Orlicz-Aleksandrov problem from the perspective of geometric flow. Furthermore, a special uniqueness result of solutions to this problem shall be discussed.
Ben Andrews classified the limiting shape for isotropic curvature flow corresponding to the solutions of the $L_p$-Minkowski problem as $p\to-\infty$ in the planar case. In this paper, we use the group-invariant method to study the…
The even Gaussian dual Minkowski problem studied by Feng, Hu and Xu, In this paper, we consider the even $L_p$ dual-Gaussian Minkowski problem for $p>1$. The existence of $o$-symmetric solution in the case $p>1$ is obtained.
In this paper, we introduce a class of new logarithmic curvature flow. The flows are designed to embrace the monotonicity of the related functional, and the convergence of this flow would tackle the solvability of the weighted…
This paper studies the general Lp dual curvature density equation under a group symmetry assumption. This geometric partial differential equation arises from the general Lp dual Minkowski problem of prescribing the Lp dual curvature measure…
We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure $\mu$ with a positive smooth density $f$, any solution to the $L_p$ Minkowski problem in $\mathbb{R}^{n+1}$ with $p \le…
In this paper, we study the long-time existence and asymptotic behavior for a class of anisotropic non-homogeneous curvature flows without global forcing terms. By the stationary solutions of such anisotropic flows, we obtain existence…
In this paper we study an anisotropic expanding flow of smooth, closed, uniformly convex hypersurfaces in $\mathbb{R}^{n+1}$ with speed $\psi\sigma_k(\lambda)^{\alpha}$, where $\alpha$ is a positive constant, $\sigma_k(\lambda)$ is the…
This is a sequel to [2] and [3], which study the second boundary value problems for mean curvature flow. Consequently, we construct the translating solitons with prescribed Gauss image in Minkowski space.
In this paper, the $q$-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the $q$-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang…
The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the…
Lutwak, Yang and Zhang \cite{LYZ2018} introduced the $L_p$ dual curvature measure that unifies several other geometric measures in dual Brunn-Minkowski theory and Brunn- Minkowski theory. Motivated by works in \cite{LYZ2018}, we consider…
This paper gives a systematic study to the general dual-polar Orlicz-Minkowski problem (e.g., Problem \ref{general-dual-polar}). This problem involves the general dual volume $\widetilde{V}_G(\cdot)$ recently proposed in \cite{GHWXY, GHXY}…
This paper studies the core problems in the $L_p$ dual Brunn-Minkowski theory, encompassing the $L_p$ Minkowski problem and $L_p$ Brunn-Minkowski inequality for dual quermassintegrals. For the case $0<p<q\leq n$, we establish $C^0$…
We study the motion of smooth, closed, strictly convex hypersurfaces in Rn+1 expanding in the direction of their normal vector field with speed depending on the k-th elementary symmetric polynomial of the principal radii of curvature. As an…