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Rigidity of Minimal Submanifolds in Hyperbolic Space

Harandi, Amir Reza | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56384 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Ranjbar Motlagh, Alireza
  7. Abstract:
  8. 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
  9. Keywords:
  10. Hyperbolic Space ; Scalar Curvature ; Total Scalar Curvature ; L2 Harmonic 1-Form ; Minimal Submanifold ; Rigidity

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