Discipline: 
Mathematics
Status: 
Available
Level: 
Honours Project
Level: 
Summer Project
Supervisor(s): 
Dr Huy The Nguyen

For Riemannian manifolds, there is a natural differential geometric operator, the Laplacian. The eigenvalues of this operator are important geometric invariants of the manifold and there are many important results which relate the eigenvalues to other geometric quantities (volume, diameter etc.). In the project you will study a number of these inequalities, their proofs and applications.