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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11804 |
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Table of Contents:
- In this paper we study non-degeneracy properties of $Σ$ via the Jacobi operator $J_Σ:=Δ_Σ+|A_Σ|^2$ of a given minimal hypersurface $Σ$ asymptotic to a cone $C\subset \mathbb{R}^{N+1}$ of co-dimension one. Here $Δ_Σ$ is the Laplace Beltrami operator of $Σ$ and $|A_Σ|$ is the norm of the second fundamental form of $Σ$. We also construct a right inverse of $J_Σ$, that is, we prove that the Jacobi equation $J_Σϕ=f$ is solvable in $Σ$, at least under some suitable non-degeneracy assumptions about $Σ$ and about the asymptotic behavior of $f$ at infinity. We also discuss some examples where our results can be applied.