The Euler derivative. An intrinsic approach to the calculus of variations.
The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids
This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either or or are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to , where is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...
The evolution of harmonic mappings with free boundaries.
The evolution of harmonic maps
The evolution of the Dirac field in cuved space-times.
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 Exterior Derivation and the Orders of Differential Forms on Contractible Algebras.
The family of isometric superconformal harmonic maps and the affine Toda equations.
The Fatou theorem for NA groups - a negative result
The Fedoryuk Condition and the Łojasiewicz Exponent near a Fibre of a Polynomial
We give a description of the set of points for which the Fedoryuk condition fails in terms of the Łojasiewicz exponent at infinity near a fibre of a polynomial.
The Feynman path integral as an improper integral over the Sobolev space
The first eigenvalue of a Riemann surface.