Translating solutions to Lagrangian mean curvature flow
56 citations recorded by the source corpus.
We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an $L^2$ bound on the mean curvature are planes and that almost-calibrated translating solutions which are static are also planes. Recent work of D. Joyce, Y.-I. Lee, and M.-P. Tsui, shows that these conditions are optimal.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/5b0df99b7502b42a8d42631ad821ebb6297d53c7
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Self-similar solutions and translating solitons for Lagrangian mean curvature flow (2008, unknown): “See also the recent work by Neves and Tian [21] for related discussions.”
- Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow (2014, unknown): “Be warned that I expect the difficulty of proving Conjectures 3.2 and 3.34 increases sharply with dimension, and even in dimension 3 is probably comparable in difficulty to the three-dimensional Poincaré Conjecture, as proved by Perelman and others (see Morgan and Tian [54]).”
- On short time existence for the planar network flow (2014, methodology): “This monotone integral quantity has already been applied by the second author in the setting of Lagrangian Mean Curvature Flow in several places, see [16, 17, 18].”