Uniqueness of some cylindrical tangent cones to special Lagrangians
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39_2023_Article_634.pdf
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Author(s)
Collins, Tristan C.
Li, Yang
Date Issued
March 13, 2023
Publisher
Springer International Publishing
Citation
Collins, Tristan C. and Li, Yang. 2023. "Uniqueness of some cylindrical tangent cones to special Lagrangians."
Version
Final published version
Abstract
Abstract
We show that if an exact special Lagrangian
$$N\subset {\mathbb {C}}^n$$
N
⊂
C
n
has a multiplicity one, cylindrical tangent cone of the form
$${\mathbb {R}}^{k}\times {\textbf{C}}$$
R
k
×
C
where
$${\textbf{C}}$$
C
is a special Lagrangian cone with smooth, connected link, then this tangent cone is unique provided
$${\textbf{C}}$$
C
satisfies an integrability condition. This applies, for example, when
$${\textbf{C}}= {\textbf{C}}_{HL}^{m}$$
C
=
C
HL
m
is the Harvey-Lawson
$$T^{m-1}$$
T
m
-
1
cone for
$$m\ne 8,9$$
m
≠
8
,
9
.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-023-00634-x
