Lagrangian F-stability of closed Lagrangian self-shrinkers

Dynamical Stability in Lagrangian

Lagrangian Probability Distribution

This article has no abstract.

Eulerian and Lagrangian stability of fluid motions

In this thesis, we study stability of inviscid fluids in the Lagrangian sense. That is, we look at how paths of particles diverge from each other under a small perturbation of the initial velocity field. The more usual question of stability is in the Eulerian sense, when one looks at how velocities at each point diverge from a steady state under a small perturbation. We demonstrate, for certain...

On stability of projections of Lagrangian varieties

We show that Lagrangian and Legendre varieties associated with matrix singularities and singularities of composite functions are stable in a sense which is a natural modification of Givental’s notion of stability of Lagrangian projections. The study of singular Lagrangian and Legendre varieties was initiated about twenty five years ago by Arnold when he was investigating singularities in the va...

Viscous Stability of Quasi-periodic Lagrangian Tori

We consider a smooth Tonelli Lagrangian L : TTn → R and its viscosity solutions u(x, P ) characterized by the cell equation H(x, P + Dxu(x, P )) = H(P ), where H : T ∗Tn → R is the Hamiltonian associated with L. We will show that if P0 corresponds to a quasi-periodic Lagrangian invariant torus, then Dxu(x, P ) is Hölder continuous in P at P0 with Hölder exponent arbitrarily close to 1, and if b...