Mathematics Dept.
  Events
UBC
Tue 1 Nov 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS (WMAX 110) (Notice the date change)
Liouville-type theorems for some elliptic equations and systems
PIMS (WMAX 110) (Notice the date change)
Tue 1 Nov 2011, 3:30pm-4:30pm

Abstract

In this talk, we consider the problem of non-existence of solutions for some basic elliptic equations and systems with weights. Starting with Henon-Lane-Emden system, we present a Liouville-type theorem for bounded solutions in dimension N=3 as well as the full Henon-Lane-Emden conjecture in higher dimensions.  Since systems are normally much more complicated than equations, in higher dimensions we back to single equations (both second order and fourth order) to prove such theorems under some additional assumptions on solutions. 
 
Also, during the talk we will see many open problems. 
 
This work has been done under supervision of N. Ghoussoub.


 
 
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UBC
Tue 15 Nov 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (Schedule and time tentative)
Free boundary problem for embedded minimal surfaces
WMAX 110 (Schedule and time tentative)
Tue 15 Nov 2011, 3:30pm-4:30pm

Abstract

For any smooth compact Riemannian 3-manifold with boundary, we prove that there always exists a smooth, embedded minimal surface with (possibly empty) free boundary. We also obtain a priori upper bound on the genus of such minimal surfaces in terms of the topology of the ambient compact 3-manifold. An interesting note is that no convexity assumption on the boundary is required. In this talk,  we will describe the min-max construction for the free boundary problem, and then we will sketch a proof of the existence part of the theory.
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