Geometrics Analysis Seminar Archives
Date  Speakers  

Friday, February 13, 2015  10:00 to 11:00

Pansu Differentiability of Lipschitz Mappings Between Carnot Groups II  
Friday, February 6, 2015  10:00 to 11:00

Pansu Differentiability of Lipschitz Mappings Between Carnot Groups I  
Friday, January 16, 2015  10:00 to 10:50

Classical Hodge Decomposition Theorem  
Friday, January 16, 2015  10:00 to 10:45

Classical Hodge Decomposition Theorem 
<p><span>I follow the proof in Chapter 6 of Frank Warner's <em>Foundations of </em></span><span><em>Differential Manifolds and Lie Groups</em> of the </span><span class="il">Hodge</span><span> Decomposition </span><span>Theorem. To state the theorem, we take an elegant generalization of </span><span>the Laplacian operator "Delta" to the LaplaceBeltrami operator on </span><span><em>p</em>forms on Riemannian manifolds. The decomposition theorem states </span><span>that this space of pforms orthogonally decomposes into the kernel and </span><span>image of the LaplaceBeltrami operator. The short but pretty proof </span><span>uses the ellipticity of the Laplace Beltrami operator together with a </span><span>RellichKondrachovtype theorem and the Hahn Banach theorem.</span></p>

Friday, October 24, 2014  09:00 to 10:00

A new proof of the structure of geodesics in higher dimensional Heisenberg groups  
Friday, October 3, 2014  09:00 to 10:00

A game interpretation of convexity preserving properties for nonlinear equations  
Friday, September 19, 2014  09:00 to 10:00

A brief introduction to the viscosity solutions  
Friday, September 12, 2014  09:00 to 10:00

A characterization of mappings of bounded length distortion  
Friday, September 5, 2014  09:00 to 10:00

Brezis Nguyen Jacobian Determinant for $W^{(N1)/N, N}$ 