The Euler and Helmholtz operators on fibered manifolds with oriented bases
We study naturality of the Euler and Helmholtz operators arising in the variational calculus in fibered manifolds with oriented bases.
The evolution of harmonic mappings with free boundaries.
The evolution of harmonic maps
The evolution of the scalar curvature of a surface to a prescribed function
We investigate the gradient flow associated to the prescribed scalar curvature problem on compact riemannian surfaces. We prove the global existence and the convergence at infinity of this flow under sufficient conditions on the prescribed function, which we suppose just continuous. In particular, this gives a uniform approach to solve the prescribed scalar curvature problem for general compact surfaces.
The existence of critical values in an abstract perturbation problem.
The existence of gaps in minimal foliations.
The existence of nonminimal regular harmonic maps from to
The existence of polar non-degenerate functions on a topological manifold
The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.
In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λ0u = f(u), u ∈ H01(Ω) in an exterior domain Ω = RnO (N ≥ 3) with O a smooth bounded and star-shaped open set, and limt→+∞ f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian.
The explicit construction of all harmonic two-spheres in G2 (Rn).
The explosion of singular cycles
The family of isometric superconformal harmonic maps and the affine Toda equations.
The Free Loop Space of Globally Symmetric Spaces.
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.