3:30 pm, Seminar Hall Compactness of the space of singular, minimal hypersurfaces with bounded volume and Jacobi eigenvalue Akashdeep Dey Princeton University. 060819 Abstract Let $\{M_k\}_{k=1}^{\infty}$ be a sequence of closed, singular, minimal hypersurfaces in a closed Riemannian manifold $(N^{n+1},g), n+1 \geq 3$. Suppose, the volumes of $M_k$ are uniformly bounded from above and the $p$th Jacobi eigenvalues of $M_k$ are uniformly bounded from below. Then, there exists a closed, singular, minimal hypersurface $M$ in $N$ with the above mentioned volume and eigenvalue bounds such that possibly after passing to a subsequence, $M_k$ weakly converges (in the sense of varifolds) to $M$. Moreover, the convergence is smooth and graphical over the compact subsets of $reg(M) \setminus Y$ where $Y$ is a finite subset of $reg(M)$ with $Y\leq p1$. This result generalizes the previous results of Sharp and AmbrozioCarlottoSharp in higher dimensions.
