# LisMath Seminar

### Chegger constants and partition problems

The Cheeger constant of a manifold (or domain), first introduced about 50 years ago, is a quantitative measure of how easily the manifold can be partitioned into two pieces. It is also closely related to the first non-trivial eigenvalue of the Laplace-Beltrami operator on the manifold and thus links partitioning problems with spectral geometry. The proposed seminar talk explores some of these connections, as well as contemporary research results giving generalisations to graphs, higher-order partitions and eigenvalues.

Bibliography:

[1] P. Buser, Ann. Sci. École Norm. Sup. (4) 15 (1982), 213-230.

[2] J. Cheeger, Problems in Analysis, Princeton Univ. Press (1970), 195-199.

[3] B. Kawohl and V. Fridman, Comm. Math. Univ. Carol. 44 (2003), 659-667.

[4] C. Lange, S. Liu, N. Peyerimhoff and O. Post, Calc. Var. PDE 54 (2015), 4165-4196.

[5] J. Lee, S. Oveis Gharan and L. Trevisan, Proc. 2012 ACM Symposium on Theory of Computing, ACM, NY (2012), 1117-1130.

[6] L. Miclo, Invent. Math. 200 (2015), 311-343.