相关论文: Bernstein theorem for translating solitons of hype…
In this paper we develop a global correspondence between immersed horospherically convex hypersurfaces in hyperbolic space and complete conformal metrics on domains in the sphere. We establish results on when the hyperbolic Gauss map is…
In this paper, we consider a Generalized Bernstein Theorem for a type of generalized minimal surfaces, namely minimal Plateau surfaces. We show that if an orientable minimal Plateau surface is stable and has quadratic area growth in…
In this paper, we investigate the parametric version and non-parametric version of rigidity theorem of spacelike translating solitons in pseudo-Euclidean space $\mathbb{R}^{m+n}_{n}$. Firstly, we classify $m$-dimensional complete spacelike…
By carrying out refined point-wise estimates for the mean curvature, we prove better rigidity theorems of Lagrangian and symplectic translating solitons.
The properties of multimomentum maps on null hypersurfaces, and their relation with the constraint analysis of General Relativity, are described. Unlike the case of spacelike hypersurfaces, some constraints which are second class in the…
We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface $X\subset \mathbb P^{n+1}$ of degree $d$ over an algebraically closed…
In this paper, we derive curvature estimates for strongly stable hypersurfaces with constant mean curvature immersed in $\mathbb{R}^{n+1}$, which show that the locally controlled volume growth yields a globally controlled volume growth if…
If the Radon transform of a compactly supported distribution $f \ne 0$ in $\mathbb R^n$ is supported on the set of tangent planes to the boundary $\partial D$ of a bounded convex domain $D$, then $\partial D$ must be an ellipsoid. As a…
Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.
We consider $n+1$ dimensional smooth Riemannian and Lorentzian spaces satisfying Einstein's equations. The base manifold is assumed to be smoothly foliated by a one-parameter family of hypersurfaces. In both cases---likewise it is usually…
We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do…
We prove the existence of rotational hypersurfaces in $\mathbb{H}^n\times \mathbb{R}$ with $H_{r+1}=0$ and we classify them. Then we prove some uniqueness theorems for $r$-minimal hypersurfaces with a given (finite or asymptotic) boundary.…
We prove a conjecture of Bernstein that the superconvexity of the heat kernel on hyperbolic space holds in all dimensions and, hence, there is an analog of Huisken's monotonicity formula for mean curvature flow in hyperbolic space of all…
The paper deals with the necessary and sufficient conditions for obtaining reconstruction formulae and sampling theorems for every function belonging to the principal shift invariant subspace of $L^2(\mathbb{H}^n)$, both in the time domain…
We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.
In this paper we describe all rotation $H$-hypersurfaces in $H^n \times R$ and use them as barriers to prove existence and characterization of certain vertical $H$-graphs and to give symmetry and uniqueness results for compact…
In this paper, we focus on a conformally flat Riemannian manifold $(M^n,g)$ of dimension $n$ isometrically immersed into the $(n+1)$-dimensional light-cone $\Lambda^{n+1}$ as a hypersurface. We compute the first and the second variational…
We derive some estimates for stable minimal hypersurfaces in $R^{n+1}$. The estimates are related to recent proofs of Bernstein theorems for complete stable minimal hypersurfaces in $R^{n+1}$ for $3\le n\le 5$ by Chodosh-Li,…
This paper may be viewed as a companion paper to [G1]. In that paper, $L^2$ Sobolev estimates derived from a Newton polyhedron-based resolution of singularities method are combined with interpolation arguments to prove $L^p$ to $L^q_s$…
This paper establishes geometric obstructions to the existence of complete, properly embedded, mean curvature flow self-translating solitons $\Sigma^n\subseteq \mathbb{R}^{n+1}$, generalizing previously known non-existence conditions such…