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This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic So...
We present a simple and direct proof of the equivalence of various functional inequalities such as Sobolev or Nash inequalities. This proof applies in the context of Riemannian or sub-elliptic geome...
Most smoothing procedures are via averaging. Pseudo-Poincar¶e in- equalities give a basic Lp-norm control of such smoothing procedures in terms of the gradient of the function involved. When av...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
Abstract: We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Conve...
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Our main result is an isoperimetric inequality for the case of a C2-smooth compact hype...
On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first s...
This paper is a corrigendum on a paper published in an earlier volume of JIPAM, 'Lower Bounds for the Infimum of the Spectrum of the Schrodinger Operator in and the Sobolev Inequalities' published in...
Lower Bounds for the Infimum of the Spectrum of the Schrödinger Operator in $\mathbb{R}^n$ and the Sobolev Inequalities.

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