Solutions of the Special Lagrangian Equation near Infinity
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_ | 1866912179819642880 |
|---|---|
| author | Han, Qing Marchenko, Ilya |
| author_facet | Han, Qing Marchenko, Ilya |
| contents | Solutions to special Lagrangian equations near infinity, with supercritical phases or with semiconvexity on solutions, are known to be asymptotic to quadratic polynomials for dimension $n\ge 3$, with an extra logarithmic term for $n=2$. Via modified Kelvin transforms, we characterize remainders in the asymptotic expansions by a single function near the origin. Such a function is smooth in even dimension, but only $C^{n-1,α}$ in odd dimension $n$, for any $α\in (0,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solutions of the Special Lagrangian Equation near Infinity Han, Qing Marchenko, Ilya Analysis of PDEs Differential Geometry Solutions to special Lagrangian equations near infinity, with supercritical phases or with semiconvexity on solutions, are known to be asymptotic to quadratic polynomials for dimension $n\ge 3$, with an extra logarithmic term for $n=2$. Via modified Kelvin transforms, we characterize remainders in the asymptotic expansions by a single function near the origin. Such a function is smooth in even dimension, but only $C^{n-1,α}$ in odd dimension $n$, for any $α\in (0,1)$. |
| title | Solutions of the Special Lagrangian Equation near Infinity |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2501.04254 |