共查询到20条相似文献,搜索用时 15 毫秒
1.
研究了在Yamabe流下演化的一个完备非紧黎曼流形,对流形上热方程的正解给出了两种局部的梯度估计.作为应用,可以得到这个热方程的Harnack不等式. 相似文献
2.
本文我们推到了黎曼流形上指数调和型热方程的一个Hamilton-Souplet-Zhang型梯度估计. 利用这个估计, 我们得到了一个Liouville型定理. 相似文献
3.
利用两种不同的方法讨论了带权流形上热方程和Schrodinger方程解的Harnack估计,先利用最大模原理证明热方程解的梯度估计,从而得到解的Harnack估计,另外利用算子半群的方法证明位势函数为常数的Schrodinger方程解的Harnack估计. 相似文献
4.
The authors obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation:αu/αt=△u-b(x,t)u~σ on complete noncompact manifolds with Ricci curvature bounded from below,where 0σ1 is a real constant,and b(x,t) is a function which is C~2 in the x-variable and C~1 in the t-variable. 相似文献
5.
Hans-Joachim Hein 《纯数学与应用数学通讯》2019,72(1):122-135
Let Y be a closed Calabi-Yau manifold. Let ω be the Kähler form of a Ricci-flat Kähler metric on . We prove that if ω is uniformly bounded above and below by constant multiples of , where is the standard flat Kähler form on and ωY is any Kähler form on Y, then ω is a product Kähler form up to a certain automorphism of . © 2018 Wiley Periodicals, Inc. 相似文献
6.
本文我们得到了黎曼流形上一类非线性抛物方程的局部Hamilton梯度估计. 利用这个局部估计,我们得到了一个Harnack型不等式和一个Liouville型定理. 相似文献
7.
Maxim Braverman 《K-Theory》2002,27(1):61-101
Let D be a (generalized) Dirac operator on a noncompact complete Riemannian manifold M acted on by a compact Lie group G. Let v: M g = Lie G be an equivariant map, such that the corresponding vector field on M does not vanish outside of a compact subset. These data define an element of K-theory of the transversal cotangent bundle to M. Hence, by embedding of M into a compact manifold, one can define a topological index of the pair (D,v) as an element of the completed ring of characters of G. We define an analytic index of (D,v) as an index space of certain deformation of D and we prove that the analytic and topological indexes coincide. As a main step of the proof, we show that index is an invariant of a certain class of cobordisms, similar to the one considered by Ginzburg, Guillemin and Karshon. In particular, this means that the topological index of Atiyah is also invariant under this class of noncompact cobordisms. As an application, we extend the Atiyah–Segal–Singer equivariant index theorem to our noncompact setting. In particular, we obtain a new proof of this theorem for compact manifolds. 相似文献
8.
Xu Qian FAN 《数学学报(英文版)》2007,23(4):623-638
We study the Poisson equation on some complete noncompact manifolds with asymptotically nonnegative curvature. We will also study the limiting behavior of the nonhomogeneous heat equation on some complete noncompact manifolds with nonnegative curvature. 相似文献
9.
In the paper, the authors provide a new proof and derive some new elliptic type (Hamilton type) gradient estimates for fast diffusion equations on a complete noncompact Riemannian manifold with a fixed metric and along the Ricci flow by constructing a new auxiliary function. These results generalize earlier results in the literature. And some parabolic type Liouville theorems for ancient solutions are obtained. 相似文献
10.
Charles S. Kahane 《Czechoslovak Mathematical Journal》2001,51(1):39-44
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex. 相似文献
11.
本文对p-Laplace Schr(o|¨)dinger热方程正连续弱解做了椭圆型梯度估计;作为应用,本文得到了一个关于p-Laplace算子的Liouville型结果;并证明了关于p-LaplaceSchr(o|¨)dinger热方程正连续弱解的Harnack不等式. 相似文献
12.
A. G. Losev 《Differential Equations》2017,53(12):1595-1604
The behavior of solutions of the Poisson equation on noncompact Riemannian manifolds of a special form is studied. Sharp conditions for the unique solvability of the Dirichlet problem on the reconstruction of solutions of the Poisson equation from continuous boundary data at infinity are found. 相似文献
13.
In this paper, the authors obtain the gradient estimates for positive solutions to the weighted p-Laplacian Lichnerowicz equation △p,fu + cuσ= 0 on noncompact smooth metric measure space, where c is a nonnegative constant, and p, σ(1 < p≤2, σ≤p-1) are real constants. Moreover, by the gradient estimate, they can get the corresponding Liouville theorem and Harnack inequality. 相似文献
14.
Chiung-Jue Anna Sung 《Journal of Geometric Analysis》2018,28(1):360-374
We establish an interior Hessian estimate for the scalar heat equation on a complete manifold with bounded curvature. Our estimate is independent of the covariant derivatives of the curvature. 相似文献
16.
This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation:u_t = △u +▽φ·▽u+a(x)uln u + b(x)u on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by- K(K ≥ 0),where φ is a C~2 function,a(x) and b(x) are C~1 functions with certain conditions. 相似文献
17.
WU Jiayong 《偏微分方程(英文版)》2010,(1):68-79
Let (M,g) be a complete non-compact Riemannian manifold with the m- dimensional Bakry-Emery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive smooth bounded solutions to the following nonlinear diffusion equation ut = △u - △↓ φ· △ ↓u - aulogu- bu,where φ is a C^2 function, and a ≠ 0 and b are two real constants. This work generalizes the results of Souplet and Zhang (Bull. London Math. Soc., 38 (2006), pp. 1045-1053) and Wu (Preprint, 2008). 相似文献
18.
我们给出关于黎曼流形上的扩散方程θtu=Δu-▽φ·▽u(这里φ是一个C^2函数)的一些梯度估计。这推广了R.Hamilton和Qi S.Zhang关于热方程的一些梯度估计。 相似文献
19.
Martin Man-chun Li 《Journal of Geometric Analysis》2014,24(3):1490-1496
Let M be a compact n-dimensional Riemannian manifold with nonnegative Ricci curvature and mean convex boundary ?M. Assume that the mean curvature H of the boundary ?M satisfies H≥(n?1)k>0 for some positive constant k. In this paper, we prove that the distance function d to the boundary ?M is bounded from above by \(\frac{1}{k}\) and the upper bound is achieved if and only if M is isometric to an n-dimensional Euclidean ball of radius \(\frac{1}{k}\) . 相似文献
20.
设M为n维完备无边界的流形,它的Ricci曲率有下界-K,这里K为实常数.假设M上的向量场B满足|B|≤γ且(△)B≤K*,这里γ为非负常数,K*为实常数,则带权Laplacian方程△u Bu=0任意正的光滑解满足最优梯度估计|(△u)|2/u2≤m(K K*) mγ2/m-n,其中任意常数m>n. 相似文献