Rigidity of minimal submanifolds in hyperbolic space
classification
🧮 math.DG
keywords
hyperbolicminimalprovespacecompletecurvaturedimensionalexist
read the original abstract
We prove that if an $n$-dimensional complete minimal submanifold $M$ in hyperbolic space has sufficiently small total scalar curvature then $M$ has only one end. We also prove that for such $M$ there exist no nontrivial $L^2$ harmonic 1-forms on $M$.
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