Compact Minimal Submanifolds in a Large Class of Riemannian Manifolds
Autor
Herrera, Jónatan
Salamanca, Juan J.
Rubio, Rafael M.
Editor
SpringerFecha
2023Materia
Minimal immersionCompact submanifold
Minimal hypersurface equation
Orthogonally splitted manifolds
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Through a new technique, we provide uniqueness, rigidity and non-existence results for compact minimal submanifolds of arbitrary dimension in a large class of Riemannian manifolds, which include between others, Riemannian double-twisted and warped products. Moreover, we show that our results can be applied in particular, to space forms and Cartan–Hadamard manifolds, re-obtaining several classic results in a different approach. Interesting applications to Geometric Analysis are also showed.