3 problems

Let $(M,g)$ be a compact Riemannian three-manifold with boundary $\partial M=\Sigma\cup S$, where $S$ and $\Sigma$ meet orthogonally, $\Sigma$ has positive Gauss curvature, and its…

Let $(M,g)$ be a manifold with boundary $\partial M=S\cup\Sigma$, where $S$ and $\Sigma$ are smooth discs meeting orthogonally along $\partial\Sigma=\partial S$. Assume that…

Let $B^n$ be the unit ball with boundary $S^{n-1}$. Let $\Sigma$ be a $k$-dimensional minimal submanifold in $B^n$ with boundary $\partial\Sigma\subset S^{n-1}$, and suppose that t…