Related papers: Capillary $L_p$-Christoffel-Minkowski problem
The paper studies the sampling discretization problem for integral norms on subspaces of $L^p(\mu)$. Several close to optimal results are obtained on subspaces for which certain Nikolskii-type inequality is valid. The problem of norms…
The famous Christoffel problem is possibly the oldest problem of prescribed curvatures for convex hypersurfaces in Euclidean space. Recently, this problem has been naturally formulated in the context of uniformly $h$-convex hypersurfaces in…
We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants,…
In the paper, we develop an $L^1_k\cap L^p_k$ approach to construct global solutions to the Cauchy problem on the non-cutoff Boltzmann equation near equilibrium in $\mathbb{R}^3$. In particular, only smallness of…
In this paper, the $\mathit{L}_{\mathit{p}}$-dual Minkowski problem of Monge-Amp\`ere type were studied for different $\mathit{p}$ and $\mathit{q}$. Some new nonuniqueness results were obtained for the range…
We construct the extension of the curvilinear summation for bounded Borel measurable sets to the $L_p$ space for multiple power parameter $\bar{\alpha}=(\alpha_1, \cdots, \alpha_{n+1})$ when $p>0$. Based on this…
We generalize a theorem by J. Choe on capillary surfaces for arbitrary 3-dimensional spaces of constant curvature. The main tools in this paper are an extension of a theorem of H. Hopf due to S.-S. Chern and two index lemmas by J. Choe.
In this paper, we establish some rigidity theorems for space-like hypersurfaces in Minkowski space by using a Weinberger-type approach with P-functions and integral identities. Firstly, for space-like hypersurfaces $M$ represented as graphs…
In this paper we deal with a stationary non-degenerate $p-$Kirchhoff type problem with critical non-linearity and a subcritical parametrized perturbation. We work on bounded domains of the Euclidean space, without any restriction on the…
As we all know, the Minkowski type problem is the cornerstone of the Brunn-Minkowski theory in Euclidean space. The Heisenberg group as a sub-Riemannian space is the simplest non-Abelian degenerate Riemannian space that is completely…
In this paper, we investigate $L^p-$boundedness of the bilinear spherical maximal function associated with a general set $E\subset\R_+$. We quantify the range of $L^p-$boundedness in terms of a dilation-invariant notion of upper Minkowski…
In this paper, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key…
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…
We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existence of nontrivial, smooth, almost properly embedded surfaces…
We prove the existence of a critical subsolution of the Hamilton-Jacobi equation which is differentiable with Lipschitz differential, improving a previous result of Fathi and Siconolfi. This text is a consolidated version with a minor…
We employ curvature flows without global terms to seek strictly convex, spacelike solutions of a broad class of elliptic prescribed curvature equations in the simply connected Riemannian spaceforms and the Lorentzian de Sitter space, where…
In this paper, we study a class of singular double phase problems defined on Minkowski spaces in terms of Finsler manifolds and with right-hand sides that allow a certain type of critical growth for such problems. Under very general…
In this paper, we investigate the existence of a "weak solutions" for a Neumann problems of $p(x)$-Laplacian-like operators, originated from a capillary phenomena, of the following form \begin{equation*}…
We show that the slicing problem holds true for subspaces of $L_p,p>2$ in the setting of arbitrary measures in place of volume. This generalizes a result of Milman for the original slicing problem.
In this paper the dual Orlicz-Minkowski problem, a generalization of the $L_p$ dual Minkowski problem, is studied. By studying a flow involving the Gauss curvature and support function, we obtain a new existence result of solutions to this…