3 papers
math.DG2026
Free boundary minimal annuli in convex balls
Dongyeong Ko, Guanhua Shao
We construct a -parameter family of properly embedded genus-zero surfaces with at most two boundary components in a Riemannian -ball. The construction is a free boundary anal…
math.DG2025
Self-expanders of positive genus
Guanhua Shao, Jiahua Zou
For a general class of cones in , we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mea…
math.DG2025
Self-shrinkers with any number of ends in by stacking
Guanhua Shao, Jiahua Zou
For each half-integer and large enough integer we construct by PDE gluing methods a self-shrinker with ends and genus . re…