Session S18 - Recent progress in non-linear PDEs and their applications

Monday, July 12, 18:00 ~ 18:50 UTC-3

Eigenvalue bounds for the Paneitz operator and its associated third-order boundary operator on locally conformally flat manifolds

Mariel Saez Trumper

Pontificia Universidad Católica, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk I will discuss bounds for the first eigenvalue of the Paneitz operator $P$ and its associated third-order boundary operator $B^3$ on four-manifolds. We restrict to orientable, simply connected, locally confomally flat manifolds that have at most two umbilic boundary components. The proof is based on showing that under the hypotheses of the main theorems, the considered manifolds are confomally equivalent to canonical models. The fact that $P$ and $B^3$ are conformal in four dimensions is key in the proof.

Joint work with Maria del Mar Gonzalez (Universidad Autonoma, Madrid, España).

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