Special Lagrangian cones

Mark Haskins

doi:10.1353/ajm.2004.0029

Special Lagrangian cones

Mark Haskins

Department of Mathematical Sciences

John Hopkins University

Research output: Contribution to journal › Article › peer-review

53 Citations (SciVal)

Abstract

We study special Lagrangian cones in ℂ ⁿ with isolated singularities especially the case n = 3. Our main result constructs an infinite family of special Lagrangian cones in ℂ ³ each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in ℂ ³ with a spherical link - any such cone must be a plane. We also construct a one-parameter family of asymptotically conical special Lagrangian submanifolds from any special Lagrangian cone.

Original language	English
Pages (from-to)	845-871
Number of pages	27
Journal	American Journal of Mathematics
Volume	126
Issue number	4
DOIs	https://doi.org/10.1353/ajm.2004.0029
Publication status	Published - Aug 2004

ASJC Scopus subject areas

General Mathematics

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10.1353/ajm.2004.0029

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title = "Special Lagrangian cones",

abstract = "We study special Lagrangian cones in ℂ n with isolated singularities especially the case n = 3. Our main result constructs an infinite family of special Lagrangian cones in ℂ 3 each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in ℂ 3 with a spherical link - any such cone must be a plane. We also construct a one-parameter family of asymptotically conical special Lagrangian submanifolds from any special Lagrangian cone.",

author = "Mark Haskins",

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AB - We study special Lagrangian cones in ℂ n with isolated singularities especially the case n = 3. Our main result constructs an infinite family of special Lagrangian cones in ℂ 3 each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in ℂ 3 with a spherical link - any such cone must be a plane. We also construct a one-parameter family of asymptotically conical special Lagrangian submanifolds from any special Lagrangian cone.

UR - https://www.scopus.com/pages/publications/3142752074

U2 - 10.1353/ajm.2004.0029

DO - 10.1353/ajm.2004.0029

M3 - Article

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SN - 0002-9327

VL - 126

SP - 845

EP - 871

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 4

ER -

Special Lagrangian cones

Abstract

ASJC Scopus subject areas

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