1,666 research outputs found
Morse index and multiplicity of min-max minimal hypersurfaces
The Min-max Theory for the area functional, started by Almgren in the early
1960s and greatly improved by Pitts in 1981, was left incomplete because it
gave no Morse index estimate for the min-max minimal hypersurface.
We advance the theory further and prove the first general Morse index bounds
for minimal hypersurfaces produced by it. We also settle the multiplicity
problem for the classical case of one-parameter sweepouts.Comment: Cambridge Journal of Mathematics, 4 (4), 463-511, 201
Uniqueness of Lagrangian Self-Expanders
We show that zero-Maslov class Lagrangian self-expanders in C^n which are
asymptotic to a pair of planes intersecting transversely are locally unique if
n>2 and unique if n=2.Comment: 32 page
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