Uniqueness of Harmonie Mappings and of Solutions of Elliptic Equations on Riemannnian Manifolds.
Unitons and their moduli.
Variational inequalities and harmonic mappings.
Variations of (para-)Hodge structures and their period maps in tt*-geometry.
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Weak compactness of solutions for fourth order elliptic systems with critical growth
We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.
Weak compactness of wave maps and harmonic maps
Weierstrass representations for harmonic morphisms on Euclidean spaces and spheres.
Критические точки многомерного функционала Дирихле
О гармонических отображениях римановых поверхностей и расслоенных многообразий
О гармонических отображениях трехмерных областей.
О некоторых лиувиллевых теоремах на некомпактных римановых многообразиях
Регурярность отображений римановых многообразий, минимизирующих многомерных функционал Дирихле