[iasmath-seminars] UPDATE: 2nd Variational Methods in Geometry Seminar will start at 3:15pm

[Kristina Phillips]

Please be advised that today's 2nd Variational Methods Seminar will begin at
3:15pm instead of 3:30pm. 

 

Variational Methods in Geometry Seminar

Topic:                    Multiplicity One Conjecture in Min-max theory

Speaker:              Xin Zhou, University of California, Santa Barbara;
Member, School of Mathematics

Time/Room:       3:15pm /Simonyi Hall 101

Abstract Link:     http://www.math.ias.edu/seminars/abstract?event=141227

 

I will present a proof with some substantial details of the Multiplicity One
Conjecture in Min-max theory, raised by Marques and Neves. It says that in a
closed manifold of dimension between 3 and 7 with a bumpy metric, the
min-max minimal hypersurfaces associated with the volume spectrum introduced
by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. 

In particular, I will discuss three main parts of the proof, including: the
formulation of multiple-parameter min-max construction for hypersurfaces
with prescribed mean curvature (PMC), an approximation scheme (by PMC
min-max theory) of min-max construction of minimal hypersurfaces for
relative homotopy class of boundaries, and a topological argument to reduce
min-max construction for free homotopy class of mod-2 cycles to that for
relative homotopy class of boundaries.

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