Lagrangian L-stability of Lagrangian translating solitons

Translating Solitons to Symplectic and Lagrangian Mean Curvature Flows

In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study properties of symplectic translating solitons. We prove that, the Kähler angle α of a symplectic translating soliton with max |A| = 1 satisfies that sup |α| > π 4 |T | |T |+1 where T is the direction in which the surface translates. Mathematics Subject Classification (2000): 53C44 (primary), 53C...

Embedded Solitons in Lagrangian and Semi-Lagrangian Systems

We develop the technique of the variational approximation for solitons in two directions. First, one may have a physical model which does not admit the usual Lagrangian representation, as some terms can be discarded for various reasons. For instance, the second-harmonic-generation (SHG) model considered here, which includes the Kerr nonlinearity, lacks the usual Lagrangian representation if one...

Dynamical Stability in Lagrangian

Translating Solutions to Lagrangian Mean Curvature Flow

We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an L 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.

Lagrangian Probability Distribution

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