# Mathematical Sciences Research Institute

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# Workshop

Geometric Evolution Equations March 12, 2007 - March 16, 2007
 Registration Deadline: March 06, 2007 about 7 years ago December 12, 2006 over 7 years ago
Parent Program: Geometric Evolution Equations and Related Topics
Organizers Bennett Chow, Gerhard Huisken, Chuu-Lian Terng, and Gang Tian
Speaker(s)

## Show List of Speakers

Description

Geometric flows have been applied to a variety of geometric, topological, analytical and physical problems. Such flows include the mean, inverse mean, Gauss curvature and Willmore flows of submanifolds, Ricci/Kähler-Ricci and Calabi flows of manifolds, Yang-Mills and Hermitian-Einstein flows of connections and metrics on vector bundles, and Yamabe and other conformal flows of metrics. Applications include the Geometrization Conjecture (in the process of verification), Penrose inequality, uniformization theorems in Kähler geometry, existence of canonical metrics, connections and maps such as Einstein, Hermitian-Einstein, constant scalar curvature, and extremal metrics, Yang-Mills connections, and harmonic maps. Techniques include the geometric theory of a priori estimates, singularity analysis, surgery techniques, weak solutions, global existence and convergence. SCHEDULE: Monday March 12 9:30 am -- 10:30 am Burkhard Wilking Manifolds with positive curvature operators are space forms 11:00 am -- 12:00 pm Natasa Sesum Title TBA 2:00 pm -- 3:00 pm Felix Schulze Nonlinear evolution by mean curvature and isoperimetric inequalities 4:10 pm -- 5:00 pm MSRI/Evans Talk 60 Evans Hall; University of California, Berkeley Robert Bryant Finsler surfaces of constant curvature Tuesday March 13 9:30 am -- 10:30 am Klaus Ecker Title TBA 11:00 am -- 12:00 pm Rafe Mazzeo CMC foliations and area-minimizing submanifolds in asymptotically hyperbolic spaces 2:00 pm -- 3:00 pm Weiyong He Title TBA 3:30 pm -- 4:30 pm Simon Brendle Title TBA Wednesday March 14 9:30 am -- 10:30 am John Lott On type-III Ricci flow solutions 11:00 am -- 12:00 pm Yuanlong Xin Convexity, Rigidity and Mean Curvature Flow 2:00 pm -- 3:00 pm Dan Knopf Title TBA 3:30 pm -- 4:30 pm Qi Zhang A Li-Yau type inequality for the conjugate heat equation under Ricci flow Thursday March 15 9:30 am -- 10:30 am Todd Oliynyk Title TBA 11:00 am -- 12:00 pm Jiayu Li Title TBA 2:00 pm -- 3:00 pm Xiuxiong Chen Title TBA 3:30 pm -- 4:30 pm Reto Mueller Differential Harnack Inequalities and Monotone Quantities Friday March 16 9:30 am -- 10:30 am Jan Metzger Title TBA 11:00 am -- 12:00 pm Andre Neves Convergence of inverse mean curvature flow in asymptotically hyperbolic manifolds Talks from Recent Developments in Numerical Methods and Algorithms for Geometric Evolution Equations will be scheduled in the afternoon and the next day (Saturday). _______________________________________________________________ Abstracts: Felix Schulze Abstract: Evolving smooth, compact hypersurfaces in R^{n+1} with normal speed equal to a positive power k of the mean curvature improves a certain 'isoperimetric difference' for k >= n-1. As singularities may develop before the volume goes to zero, we develop a weak level-set formulation for such flows and show that the above monotonicity is still valid. This proves the isoperimetric inequality for n <= 7. Extending this to complete, simply connected 3-dimensional manifolds with nonpositive sectional curvature, we give a new proof for the Euclidean isoperimetric inequality on such manifolds. Andre Neves Abstract: I will show that inverse mean curvature flow does not have the asymptotic convergence needed to prove a Penrose-type inequality for asymptotically hyperbolic 3-manifolds.

A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: K70000. The cut-off date for reservations is February 9, 2007. A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. The following Group Code should be entered in the "Comment" field when booking through our Website. Group Code = CGMS38. Please note: The Original Queen room type does not have an in-room T1 connection, but we do have WIFI available in our main lobby area. The cut-off date for reservations is February 9, 2007. The funding deadline has passed. Late funding requests will be considered only if additional funds become available.

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

## Show Visa/Immigration

Schedule
Mar 12, 2007
Monday
 09:30 AM - 10:30 AM Manifolds with Positive Curvature Operators are Space Forms. Burkhard Wilking 11:00 AM - 12:00 PM TBA Natasa Sesum (Rutgers University) 02:00 PM - 03:00 PM Nonlinear Evolution By Mean Curvature and Isoperimetric Inequalities Felix Schulze
Mar 13, 2007
Tuesday
 09:30 AM - 10:30 AM TBA Klaus Ecker 11:00 AM - 12:00 PM CMC Folliations and Area-Minimizing Submanifolds in Asymptotically Hyperbolic Spaces Rafe Mazzeo (Stanford University)
Mar 14, 2007
Wednesday
 11:00 AM - 12:00 PM Convexity, Rigidity and Mean Curvature Flow Yuan-Long Xin 02:00 PM - 03:00 PM TBA Dan Knopf 03:30 PM - 04:30 PM A Li-Yau Type INequality for the Conjugate Heat Equation Under Ricci Flow Qi Zhang
Mar 15, 2007
Thursday
 09:30 AM - 10:30 AM TBA Todd Oliynyk (Monash University) 11:00 AM - 12:00 PM TBA Jiayu Li 02:00 PM - 03:00 PM TBA Xiu-Xiong Chen 03:30 PM - 04:30 PM Differential Harnack Inequalities and Monotone Quantities Reto Mueller
Mar 16, 2007
Friday
 09:30 AM - 10:30 AM TBA Jan Metzger 11:00 AM - 12:00 PM Convergence of Inverse Mean Curvature Flow in Asymptotically Hyperbolic Manifolds Andre Neves (Imperial College, London)