PIMS Workshop on Geometric Analysis
- Date: 04/26/2011
Tobias Lamm (University of Frankfurt)
Reto Muller (Scuola Normale Superiore di Pisa)
Yuxiang Li (Tshinghua University/UBC)
University of British Columbia
Geometric Analysis
The focus will be on harmonic maps and Willmore surfaces.
It should be beneficial to graduate students, PDFs and faculty members in related research areas to hear these talks.
This conference follows the 5-day meeting at BIRS on geometric evolution equations and physics on April 17-22.
Speaker: Tobias Lamm
Title: Small surfaces of Willmore type in Riemannian manifolds
Speaker: Reto Mueller
Title: Ricci flow coupled with harmonic map flow
Abstract: We investigate a coupled system of the Ricci flow on M with the harmonic map flow of a map from M to some closed target manifold N. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of the map a-priori by choosing a coupling constant large enough. Moreover, it suffices to bound the curvature of (M, g(t)) to also obtain control of the evolving map and all its derivatives. Besides these new phenomena, the flow shares many good properties with the Ricci flow. In particular, we can derive the monotonicity of an energy, an entropy and a reduced
volume functional.
Speaker: Yuxiang Li
Title: Conformal immersions and its application to Willmore functional
Abstract: We study sequences a conformally immersed, compact Riemann surfaces sequence with fixed genus and bounded Willmore energy. We will show that: 1.If the conformal class sequence converges in moduli space, then the surface sequence will converges in the weakly $W^{2,2}$ sense; 2. If it diverges in moduli space, then the limit of Willmore energies must be greater than or equal to $\min(8\pi,\omega^n_p)$.
As applications, we will imply the existence of minimizer of Willmore energy in a fixed conformal class and give a new proof of the existence of minimizing Willmore surfaces of prescribed genus.
Venue: WMAX 110
09:30 - 10:30 Tobias Lamm
10:30 - 10:45 Coffee Break
10:45 - 11:45 Reto Muller
14:00 - 15:00 Yuxiang Li
Jingyi Chen (University of British Columbia)