Self-similar solutions and translating solitons for Lagrangian mean curvature flow

By D. Joyce, Ynging Lee, Mao-Pei Tsui. 2008

87 citations recorded by the source corpus.

We construct many self-similar and translating solitons for Lagrangian mean curvature flow, including self-expanders and translating solitons with arbitrarily small oscillation on the Lagrangian angle. Our translating solitons play the same role as cigar solitons in Ricci flow, and are important in studying the regularity of Lagrangian mean curvature flow. Given two transverse Lagrangian planes R^n in C^n with sum of characteristic angles less than pi, we show there exists a Lagrangian self-expander asymptotic to this pair of planes. The Maslov class of these self-expanders is zero. Thus they can serve as local models for surgeries on Lagrangian mean curvature flow. Families of self-shrinkers and self-expanders with different topologies are also constructed. This paper generalizes the work of Anciaux, Joyce, Lawlor, and Lee and Wang.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f10f1c990b3186e4eb7fbc93726c44d01b99f76a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Knut Smoczyk
2. A. Neves
3. G. Tian
4. G'abor Sz'ekelyhidi
5. Robert J. Berman
6. Song Sun
7. B. Weinkove
8. Valentino Tosatti

In Geometry and Topology

1. Knut Smoczyk
2. A. Neves
3. G. Tian
4. G'abor Sz'ekelyhidi
5. Robert J. Berman
6. Chi Li
7. Song Sun
8. B. Weinkove

In Mathematical Physics

1. Knut Smoczyk
2. A. Neves
3. G. Tian
4. Chi Li
5. Y. Xin
6. Qi Ding
7. M. Mars

Citations in the corpus

• Translating solutions to Lagrangian mean curvature flow (2007, background): “In a surprising new result, Dominic Joyce, Yng-Ing Lee, and Mao-Pei Tsui [4] found translating solutions to Lagrangian mean curvature flow with oscillation of License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use the Lagrangian angle arbitrarily ”
• Mean Curvature Flow in Higher Codimension: Introduction and Survey (2011, methodology): “Recently there has been done quite some work on the formation and classification of singularities in mean curvature flow [5,11,12,23, 25, 39, 47, 54, 56, 58, 59, 61, 71], partially motivated by Hamilton’s and Perelman’s [45, 66–68] work on the Ricci flow that in many ways behaves akin to the mean cu”