Márcio Batista

Morse index, topology, and ends of minimal surfaces with noncompact free boundary

We establish index estimates for complete two-sided free boundary minimal surfaces in smooth mean-convex domains of $\mathbb{R}^3$ with noncompact boundary. We first prove $3{\rm Ind}_s(\Sigma)\geq 2g+b-1$, where $g$ and $b$ describe the conformal compactification. We then include all interior ends with their multiplic...