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We unify the formulation and analysis of Galerkin and Runge{Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate sol...
We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge{Kutta Collocation (RK-C) methods and the continuous ...
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution o...
Hypoelliptic estimates in radiative transfer.
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on a...
Let $\Phi:TM\to TM$ be a positive-semidefinite operator of class $C^1$ defined on a complete noncompact manifold $M$ isometrically immersed in a Hadamard space $\bar{M}$. In this paper, we given condi...
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
Abstract: We give a maximum principle proof of interior derivative estimates for the K\"ahler-Ricci flow, assuming local uniform bounds on the metric.
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace theory that play a prominent role in analytic approaches to symplectic topology. These include relations...
We propose an approximation of the asymptotic variance that removes a certain discontinuity in the formula for the raw and the smoothed periodogram in case a data taper is used. It is based on an appr...
We consider hypersurfaces S \subset \RR3 with zero Gaussian curvature at every ordinary point with surface measure dS and define the surface measure dm = y(x)dS(x) for smooth function y with compact s...

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