Monthly Archives: September 2014

Notes of Karl-Theodor Sturm’s IHP 2014 lecture

Metric measure spaces with synthetic Ricci curvature bounds: state of the art 1. Requirements and definitions Equivalent to in Riemanian case Stable under convergence Intrinsic, synthetic. Bibliography Sturm, Lott Villani Sturm and many coauthors Ambrosio-Gigli-Savaré Erbar-Kuwada-Sturm : equivalence of Eulerian … Continue reading

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Notes of Andrea Bonfiglioli’s lecture

Maximal principles and Harnack inequalities for PDO’s in divergence form 1. Motivation CR geometry (sub-Laplacians), stochastic PDE’s. 2. Introduction 2.1. Standing assumptions Total nondegeneracy. Smooth hypoellipticity. Sometimes, we require that is hypoelliptic as well. Or even existence of a global, … Continue reading

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Pierre Pansu’s slides on Differential Forms and the Hölder Equivalence Problem

Here is the completed set of slides CIRMsep14_beamer If you want to know more about the construction of horizontal submanifolds and how Gromov uses it to bound Hausdorff dimensions from below, see Pansu’s Trento notes (2005).

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Notes of Anton Thalmaiers’s lecture nr 4

1. Probabilistic content of Hörmander’s condition 1.1. Statement Theorem 1 Suppose that the Lie algebra generated by and brackets fills . Then the bilinear form on is non-degenerate 1.2. Proof Let By Blumenthal’s 0/1-law, is not random. We prove by … Continue reading

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Notes of Anton Thalmaier’s lecture nr 3

1. Stochastic flows of diffeomorphisms We continue our study of SDE . Up to now, the starting point was fixed. Now we exploit the dependance on . 1.1. Random continuous paths of diffeomorphisms Let us introduce the random set of … Continue reading

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Notes of Nicola Garofalo’s lecture nr 4

1. The isoperimetric problem I want to show how PDE results can be used to solve geometric problems. 1.1. The isoperimetric inequality I will prove the isoperimetric inequality in Carnot groups, It has lots of applications, see the conference in … Continue reading

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Notes of Ludovic Rifford’s lecture nr 4

Open problems The Sard conjecture Regularity of geodesics Small balls 1. The Sard conjecture 1.1. Statement Theorem 1 (Morse 1939 for , Sard 1942) If is of class , and this is sharp (Whitney). Does this theorem generalize to the … Continue reading

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