Existence and Partial Regularity Results for the Heat Flow for Harmonic Maps.
Existence and regularity results for the gradient flow for -harmonic maps.
Expansion of embedded curves with tuning angle greater than - ... .
Forced periodic oscillations in the climate system via an energy balance model
Formules de Lefschetz délocalisées
Functional integral solution of the complex diffusion equation with complex quadratic potential in a classical path space.
Geometric Fokker-Planck equations.
Geometric heat kernel coefficient for APS-type boundary conditions
I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.
Gradient estimates, Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields.
Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds
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.
Group method analysis of two-dimensional plate in heat flux.
Harmonic analysis on fractal spaces
Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
Harmonic map Heat Flow for axially symmetric Data.
Harmonic mappings into manifolds with boundary
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
Harnack inequalities on a manifold with positive or negative Ricci curvature.
Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.
Heat diffusion on homogeneous trees (Note on a paper by G. Medolla and A. G. Setti)
Medolla e Setti [6] studiano l'andamento della diffusione del calore generata dal Laplaciano discreto su un albero omogeneo e dimostrano che il calore è asintoticamente concentrato in «anelli» che viaggiano verso l'infinito a velocità lineare e la cui larghezza divisa per tende all'infinito, dove è il tempo. Qui si spiega come un risultato più preciso si ottiene come corollario della legge dei grandi numeri e del teorema del limite centrale per la passeggiata aleatoria sull'albero. Inoltre,...
Heat flow for the equation of surfaces with prescribed mean curvature.
Heat flows for extremal Kähler metrics
Let be a closed polarized complex manifold of Kähler type. Let be the maximal compact subgroup of the automorphism group of . On the space of Kähler metrics that are invariant under and represent the cohomology class , we define a flow equation whose critical points are the extremal metrics,i.e.those that minimize the square of the -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its...