Department of Mathematics

Details

Ricci flow and the determinant of the Laplacian on non-compact manifolds

by Frederic Rochon  (www) | University of Toronto
Time: 12:10  (Thursday, Apr. 08, 2010)
Location: FI210, Fields Institute, 222 College St
Abstract:
After introducing the notion of determinant of the Laplacian on a non-compact surface with ends asymptotically isometric to a cusp or a funnel, we will show that in a given conformal class (with 'renormalized area' fixed), this determinant is maximal for the metric of constant scalar curvature, generalizing a well-known result of Osgood, Phillips and Sarnak in the compact case. This will be achieved by combining a corresponding Polyakov formula with some long time existence result for the Ricci flow for such metrics. This is a joint work with P. Albin and C.L. Aldana.

Dates in this series

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· Thursday, Jan. 14, 2010: Competing Symmetries and convergence of sequences of random symmetrizations  (Almut Burchard)

· Thursday, Jan. 21, 2010: Minimal Navier-Stokes Singularities (Ian Zwiers)

· Thursday, Jan. 28, 2010: New examples on spaces of negative sectional curvature satisfying Ma-Trudinger-Wang conditions (Jiayong Li)

· Thursday, Feb. 25, 2010: The multi-marginal optimal transportation problem (Brendan Pass)

· Thursday, Mar. 04, 2010: Rectifiability of optimal transportation plans (Brendan Pass)

· Thursday, Mar. 11, 2010: Almost Sure Local Well-posedness for the Stochastic KdV-Burgers Equation (Geordie Richards)

· Thursday, Apr. 01, 2010: On the speed of the propagation of the thin film interface (Marina Chugunova)

· Thursday, Apr. 08, 2010: Ricci flow and the determinant of the Laplacian on non-compact manifolds (Frederic Rochon)

· Thursday, Apr. 15, 2010: Ricci flow and the determinant of the Laplacian on non-compact manifolds, Part 2 (Frederic Rochon)

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· Wednesday, Jul. 14, 2010: Regularity of optimal transportation maps on multiple products of spheres (Young-Heon Kim)

· Friday, Jul. 23, 2010: Asymptotics of fast diffusion via dynamical systems (Jochen Denzler)

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· Thursday, Oct. 07, 2010: Regularity of solutions for a variational problem related to the Rochet-Chone model (Shibing Chen)

· Thursday, Oct. 21, 2010: A Generalized Euler-Lagrange Equation for the Principal-Agent Problem (Quentin Merigot)

· Thursday, Oct. 28, 2010: Global regularity of the reflector problem (Jiakun Liu)

· Thursday, Feb. 17, 2011: Sharp new conformally invariant integral inequalities (Shibing Chen)

· Thursday, Mar. 24, 2011: Aharonov--Bohm Effect in Resonances of Magnetic Schrodinger Operators with Potentials with Supports at Large Separation (Ivana Alexandrova)

· Thursday, Mar. 31, 2011: Global well-posedness for KdV in L2 (Jordan Bell)

· Thursday, Apr. 07, 2011: Structural results on optimal transportation plans (Brendan Pass)

· Thursday, Sep. 22, 2011: Rayleigh--Benard convection. A new bound on the Nusselt number (Christian Seis)

· Thursday, Sep. 29, 2011: Density functional theory and optimal transportation with Coulomb cost (Codina Cotar)

· Thursday, Oct. 06, 2011: Gradient flow methods for thin-film and related higher order equations (Ehsan Kamalinejad)

· Thursday, Oct. 13, 2011: OPTIMAL TRANSPORTATION WITH CAPACITY CONSTRAINTS (Jonathan Korman)

· Thursday, Oct. 20, 2011: Conductivity imaging from one interior measurement in the presence of perfectly conducting and insulating inclusions (Amir Moradifam)

· Thursday, Oct. 27, 2011: Loss of compactness and bubbling for complete minimal surfaces in hyperbolic space (Spryos Alexakis)

· Thursday, Nov. 03, 2011: On the coarsening rates in demixing binary viscous liquids (Christian Seis)

· Thursday, Nov. 10, 2011: Optimal transportation with infinitely many marginals (Brendan Pass)

· Thursday, Nov. 17, 2011: On uniqueness of the waiting-time type solution of the thin film equation (Marina Chugunova)

· Thursday, Nov. 24, 2011: Higher-order time asymptotics of fast diffusion in Euclidean space: a dynamical systems approach (Robert McCann)

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· Thursday, Mar. 01, 2012: Well-posedness and finite-time blowup for the Zakharov system on two-dimensional torus (Nobu Kishimoto)

· Thursday, Mar. 08, 2012: A Generalized Representation Formula for Covariant Tensor Wave Equations on Curved Spacetimes (Arick Shao)

· Thursday, Mar. 29, 2012: Big frequency cascades in the cubic nonlinear Schrödinger flow on the 2-torus (James Colliander)