The generalized Conley index and multiple solutions of semilinear elliptic problems.
The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular curve and a stratified Morse function . In this note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of .
The geometry of pseudo harmonic morphisms.
The Gluck and Ziller problem with the euclidean metric
The gradient flow of Higgs pairs
We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle over a Kähler surface , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point of this functional. We also prove that the limiting Higgs pair can be extended smoothly to a vector bundle over...
The heat equation and harmonic maps of complete manifolds.
The heat flows and harmonic maps of complete noncompact Riemannian manifolds.
The Holomorphic or Anti-Holomorphic Character of Harmonic Maps into Irreducible Compact Quotients of Polydiscs.
The index of the second variation of a control system
The information metric on rational maps.
The Lagrange complex
The Lagrange Intersections for (CPn, RPn).
The Landau-Lifshitz equation with the external field - a new extension for harmonic maps with values in S2.
The minimal period problem of classical hamiltonian systems with even potentials
The Nonlinear Connections and Harmonicity.
The number of buckled states of circular plates
The number of critical points in Morse approximations
The Rate of Convergence of a Harmonic Map at a Singular Point.
The rectifiable distance in the unitary Fredholm group
Let = u: u unitary and u-1 compact stand for the unitary Fredholm group. We prove the following convexity result. Denote by the rectifiable distance induced by the Finsler metric given by the operator norm in . If and the geodesic β joining u₀ and u₁ in satisfy , then the map is convex for s ∈ [0,1]. In particular, the convexity radius of the geodesic balls in is π/4. The same convexity property holds in the p-Schatten unitary groups = u: u unitary and u-1 in the p-Schatten class...
The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions
We first discuss a class of inequalities of Onofri type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than . Without symmetry assumption, it holds if and only if the parameter is in the interval . The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Caffarelli-Kohn-Nirenberg inequality, in two space dimensions. In fact, for suitable sets of parameters (asymptotically...