## Departmental PhD Thesis Exam – Tracey Balehowsky

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Friday, May 19, 2017
11:10 a.m.
BA6183

PhD Candidate:  Tracey Balehowsky
Thesis title:  Recovering a Riemannian Metric from Knowledge of the Areas of Properly-Embedded, Area-Minimizing Surfaces

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Abstract:

In this thesis, we prove that if $(M,g)$ is a $C^3$-smooth, 3-dimensional Riemannian manifold with mean convex boundary $\partial M$, which is additionally either a) $C^2$-close to Euclidean or b) $\epsilon_0$-thin, then knowledge of the least areas circumscribed by a simple closed curve $\gamma \subset \partial M$ and all perturbations $\gamma(t)\subset \partial M$ uniquely determines the metric. In the case where $(M,g)$ only has strictly mean convex boundary at a point $p\in\partial M$, we prove that knowledge of the least areas circumscribed by a simple closed curve $\gamma \subset U$ and all perturbations $\gamma(t)\subset U$ in a neighbourhood $U\subset \partial M$ of $p$ uniquely determines the metric near $p$.