Abstract
Let \(\Sigma ^2 \subset M^3\) be a minimal surface of index 0 or 1. Assume that a neighborhood of \(\Sigma \) can be foliated by constant mean curvature (cmc) hypersurfaces. We use min–max theory and the catenoid estimate to construct \(\varepsilon \)-cmc doublings of \(\Sigma \) for small \(\varepsilon > 0\). Such cmc doublings were previously constructed for minimal hypersurfaces \(\Sigma ^n \subset M^{n+1}\) with \(n+1\ge 4\) by Pacard and Sun using gluing methods.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have