## View abstract

### 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. document.getElementById('cloak559ef31c463bf90aed28a215338761ea').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy559ef31c463bf90aed28a215338761ea = 'm&#97;r&#105;&#101;l' + '&#64;'; addy559ef31c463bf90aed28a215338761ea = addy559ef31c463bf90aed28a215338761ea + 'm&#97;t' + '&#46;' + '&#117;c' + '&#46;' + 'cl'; var addy_text559ef31c463bf90aed28a215338761ea = 'm&#97;r&#105;&#101;l' + '&#64;' + 'm&#97;t' + '&#46;' + '&#117;c' + '&#46;' + 'cl';document.getElementById('cloak559ef31c463bf90aed28a215338761ea').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy559ef31c463bf90aed28a215338761ea + '\'>'+addy_text559ef31c463bf90aed28a215338761ea+'<\/a>';

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.