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Exsitence of metrics maximizing the first eigenvalue on closed surfaces

Posted in
Speaker: 
Henrik Matthiesen
Affiliation: 
MPI
Date: 
Thu, 2017-09-14 17:00 - 17:30
Location: 
MPIM Lecture Hall

We show that on each closed surface of fi xed topological type, orientable or non-orientable, there is a metric, smooth away from finitely many conical singularities, that maximizes the fi rst eigenvalue among all unit volume metrics. The key new ingredient are several monotonicity results relating the corresponding maximal eigenvalues. This is joint work with Anna Si ffert.

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