1,721,009 research outputs found
and operator norm estimates for the complex time heat operator on homogeneous trees
No full textLet X be a homogeneous tree of degree greater than or equal to three. In this paper we study the complex time heat operator Hζ induced by the natural Laplace operator on X. We prove comparable upper and lower bounds for the Lp norms of its convolution kernel hζ and derive precise estimates for the Lp-Lr operator norms of Hζ for ζ belonging to the half plane Re ζ ≥ 0. In particular, when ζis purely imaginary, our results yield a description of the mapping properties of the Schrödinger semigroup on X. ©1998 American Mathematical Society
Eigenvalue estimates for the Laplacian with lower order terms on a compact Riemannian manifold.
No full textProc. Sympos. Pure Math., 54, Part 3, Amer. Math. Soc., Providence, RI, 1993
A lower bound for the spectrum of the Laplacian in terms of sectional and Ricci curvature.
No full text
Global divergence theorems in nonlinear PDEs and geometry
No full textWe overview some L p -extensions of the classical divergence theorem to non-compact Riemannian manifolds without boundary. The red wire connecting all these extensions is represented by the notion of parabolicity with respect to the p-Laplace operator. It is a non-linear differential operator which is naturally related to the p-energy of maps and, therefore, to L p -integrability properties of
vector fields. To show the usefulness of these tools, a certain number of applications both to (systems of) PDEs and to the global geometry of the underlying manifold are presented. These lecture notes contain, in a slightly expanded form, the material presented at the Summer School in Di erential Geometry held in January 2012 in the Universidade Federal do Ceara-UFC, Fortaleza.
The course aims at giving an overview of some Lp-extensions of the classical divergence theorem to non-compact Riemannian manifolds without boundary
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