## View abstract

### Session S38 - Geometric Potential Analysis

Monday, July 19, 17:15 ~ 17:45 UTC-3

## On the fundamental gap of convex sets in hyperbolic space

### Alina Stancu

#### Concordia University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak3351774fe31d162f15fbcdea141b6181').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy3351774fe31d162f15fbcdea141b6181 = '&#97;l&#105;n&#97;.st&#97;nc&#117;' + '&#64;'; addy3351774fe31d162f15fbcdea141b6181 = addy3351774fe31d162f15fbcdea141b6181 + 'c&#111;nc&#111;rd&#105;&#97;' + '&#46;' + 'c&#97;'; var addy_text3351774fe31d162f15fbcdea141b6181 = '&#97;l&#105;n&#97;.st&#97;nc&#117;' + '&#64;' + 'c&#111;nc&#111;rd&#105;&#97;' + '&#46;' + 'c&#97;';document.getElementById('cloak3351774fe31d162f15fbcdea141b6181').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy3351774fe31d162f15fbcdea141b6181 + '\'>'+addy_text3351774fe31d162f15fbcdea141b6181+'<\/a>';

The difference between the first two eigenvalues of the Dirichlet Laplacian on convex sets of ${\mathbb{R}}^n$ and, respectively ${\mathbb{S}}^n$, satisfies the same strictly positive lower bound depending on the diameter of the domain. In work with collaborators, we have found that the gap of the hyperbolic space on convex sets behaves strikingly different even if a stronger notion of convexity is employed. This is very interesting as many other features of first two eigenvalues behave in the same way on all three spaces of constant sectional curvature.