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&nbsp;</em></span><span><em>Differential Manifolds and Lie Groups</em> of the&nbsp;</span><span class="il">Hodge</span><span>&nbsp;Decomposition&nbsp;</span><span>Theorem.&nbsp; To state the theorem, we take an elegant generalization of&nbsp;</span><span>the Laplacian operator "Delta" to the Laplace-Beltrami operator on&nbsp;</span><span><em>p</em>-forms on Riemannian manifolds.&nbsp; The decomposition theorem states&nbsp;</span><span>that this space of p-forms orthogonally decomposes into the kernel and&nbsp;</span><span>image of the Laplace-Beltrami operator.&nbsp; The short but pretty proof&nbsp;</span><span>uses the ellipticity of the Laplace Beltrami operator together with a&nbsp;</span><span>Rellich-Kondrachov-type 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 $W^{(N-1)/N, N}$