Bifurcation of periodic solutions to the singular Yamabe problem on spheres

Bianca Santoro

http://www.sci.ccny.cuny.edu/~bsantoro/

Date(s) : 12/05/2014   iCal
14 h 00 min - 15 h 00 min

In this talk, we describe how to obtain uncountably many periodic solutions to the singular Yamabe problem on a round sphere, that blow up along a great circle.

These are (complete) constant scalar curvature metrics on the complement of a circle inside S^m, m greater than 5, that are conformal to the round (incomplete) metric and periodic in the sense of being invariant under a discrete group of conformal transformations.

Furthermore, for 5 ≤ m ≤ 7, the solutions come from bifurcating branches of constant scalar curvature metrics on the compact quotient.

This is joint work with R. Bettiol (Notre Dame) and P. Piccione (USP).

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