In this paper, we give some examples which point to the non-existence of -global stable diagrams , compact. If : is fixed we define the -equivalence for maps and the corresponding -stability. The globalization procedure works and we can compare the -stability, -infinitesimal stability, and -homotopical stability. Also we give some characterization theorems for lower dimensions.
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.
Let be a complete noncompact Riemannian manifold. We consider gradient estimates on positive solutions to the following nonlinear equation in , where , are two real constants and , is a smooth real valued function on and . When is finite and the -Bakry-Emery Ricci tensor is bounded from below, we obtain a gradient estimate for positive solutions of the above equation. Moreover, under the assumption that -Bakry-Emery Ricci tensor is bounded from below and is bounded from above,...
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface....
In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds for the following general heat equation where is a constant and is a differentiable function defined on . We suppose that the Bakry-Émery curvature and the -dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently.
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Nous étudions les trajectoires du gradient sous-riemannien (appellé horizontal) de fonctions polynômes. Dans ce cadre l’inégalité de Łojasiewicz n’est pas valide et une trajectoire du gradient horizontal peut être de longueur infinie, et peut même s’accumuler sur une courbe fermée. Nous montrons que ces comportement sont exceptionnels ; et que, pour une fonction générique les trajectoires de son gradient horizontal ont des propriétés similaires au cas du gradient riemannien. Pour obtenir la finitude...