Monthly Archives: September 2014

Notes of Nicola Garofalo’s lecture nr 3

1. Fundamental solutions Exercise (related to the Hopf-Rinow): compute the sub-Riemannan metric associated to vectorfield . Observe that balls are non compact, i.e. metric is not complete. 2. Existence Theorem 1 (Folland) On a Carnot group, all sub-Laplacians have a … Continue reading

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Notes of Ludovic Rifford’s lecture nr 3

1. A closer look at singular curves Today’s lecture will be full of examples. 1.1. Singularity criterion Remember that when concatenating curves, if one of them is regular, the full curve is as well. So if a curve is singular, … Continue reading

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Pansu’s slides, september 1-5, 2014

Here are Pansu’s slides (version sept. 3rd, 00:13) CIRMsep14_beamer

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Notes of Anton Thalmayer’s lecture nr 2

1. -diffusions and the heat equation The problem: given a continuous function , find a solution , , of Assume is an -diffusion with lifetime . Then is an -diffusion, where . Hypothesis: assume that the lifetime is almost surely … Continue reading

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Notes of Anton Thalmaier’s lecture nr 1

The geometry of subelliptic diffusions 1. Stochastic flows Let be a vectorfield with flow . For compactly supported functions , Can one attach a flow to a second order operator ? E.g. to Basic example is the Euclidean Laplacian. Answer … Continue reading

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Notes of Nicola Garofalo’s lecture nr 2

1. Stratified nilpotent groups aka Carnot groups. 1.1. Examples: Heisenberg groups It was known to physicists under the name Weyl’s group. It was re-christened Heisenberg group by Elias Stein and his school of harmonic analysis. is a multiplication on . … Continue reading

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Notes of Ludovic Rifford’s lecture nr 2

1. Sub-Riemannian geodesics 1.1. Sub-Riemannian structures A sub-Riemannian structure is the data of a manifold , a smooth distribution of subspaces of constant rank , and a smoothly varying scalar product on . Example: restriction of a Riemannian metric to … Continue reading

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