Hierarchy structures in finite index CMC surfaces.

Meeks III, William H.; Pérez, Joaquín

Given ε 0 > 0 , I ∈ ℕ ∪ { 0 } and K 0 , H 0 ≥ 0 , let X be a complete Riemannian 3-manifold with injectivity radius Inj ⁡ (X) ≥ ε 0 and with the supremum of absolute sectional curvature at most K 0 , and let M ↬ X be a complete immersed surface of constant mean curvature H ∈ [ 0 , H 0 ] with index at most I. For such M ↬ X , we prove a structure theorem which describes how the interesting ambient geometry of the immersion is organized locally around at most I points of M, where the norm of the second fundamental form takes on large local maximum values.

MINIMAL surfaces; CURVATURE; GEOMETRY

Advances in Calculus of Variations, 2024, Vol 17, Issue 4, p1219

1864-8258

Academic Journal

10.1515/acv-2022-0113