Fredholm properties of the jacobi Operator of minimal conical hypersurfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914199541645312 |
|---|---|
| author | Rico, Oscar Ivan Agudelo Rizzi, Matteo |
| author_facet | Rico, Oscar Ivan Agudelo Rizzi, Matteo |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fredholm properties of the jacobi Operator of minimal conical hypersurfaces Rico, Oscar Ivan Agudelo Rizzi, Matteo Differential Geometry Analysis of PDEs 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. |
| title | Fredholm properties of the jacobi Operator of minimal conical hypersurfaces |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2512.11804 |