Geometry & Topology

Lagrangian mean curvature flow of Whitney spheres

Andreas Savas-Halilaj and Knut Smoczyk

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Abstract

It is shown that an equivariant Lagrangian sphere with a positivity condition on its Ricci curvature develops a type-II singularity under the Lagrangian mean curvature flow that rescales to the product of a grim reaper with a flat Lagrangian subspace. In particular this result applies to the Whitney spheres.

Article information

Source
Geom. Topol., Volume 23, Number 2 (2019), 1057-1084.

Dates
Received: 4 April 2018
Accepted: 13 July 2018
First available in Project Euclid: 17 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.gt/1555466435

Digital Object Identifier
doi:10.2140/gt.2019.23.1057

Mathematical Reviews number (MathSciNet)
MR3939057

Zentralblatt MATH identifier
07056058

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Keywords
Lagrangian mean curvature flow equivariant Lagrangian submanifolds type-II singularities

Citation

Savas-Halilaj, Andreas; Smoczyk, Knut. Lagrangian mean curvature flow of Whitney spheres. Geom. Topol. 23 (2019), no. 2, 1057--1084. doi:10.2140/gt.2019.23.1057. https://projecteuclid.org/euclid.gt/1555466435


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