Abstract: We investigate the relation between boundary data of a compact manifold and its interior geometry. A compact Riemannian manifold $D$ with smooth boundary $\del D$ is boundary rigid if its interior geometry is uniquely determined by $\del D$ and distances between points on $\del D$. $D$ is a minimal filling if for any $D'$ with $\del D'=\del D$, having larger distances between points on $\del D$ implies $\vol(D')\geq\vol(D)$.

In this thesis, we generalize D. Burago and S. Ivanov's work \cite{Burago2} on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and hence boundary rigid. This includes perturbations of real, complex, quaternionic and Cayley hyperbolic metrics.

Hybrid Defense:
Angell Hall 2163
Zoom link: https://umich.zoom.us/j/97495692365?pwd=RG5BSTJyb3Z4QzlWWGxicmU4bTJwZz09
Meeting ID: 974 9569 2365
Passcode: ruanypdef