Harmonic tori in spheres and complex projective spaces.
Harmonic -morphisms.
Harmonicity of horizontally conformal maps and spectrum of the Laplacian.
Harmonicity of vector fields on four-dimensional generalized symmetric spaces
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.
Harmonie Mappings and Kähler Manifolds.
Harnack’s inequalities for solutions to the mean curvature equation and to the capillarity problem
Hausdorff measures and the Morse-Sard theorem.
Let F : U ⊂ Rn → Rm be a differentiable function and p < m an integer. If k ≥ 1 is an integer, α ∈ [0, 1] and F ∈ Ck+(α), if we set Cp(F) = {x ∈ U | rank(Df(x)) ≤ p} then the Hausdorff measure of dimension (p + (n-p)/(k+α)) of F(Cp(F)) is zero.
Hausdorff measures of the set of critical values of functions of the class
Heat flow and boundary value problem for harmonic maps
Heat flow for the equation of surfaces with prescribed mean curvature.
Heat flow of p-harmonic maps with values into spheres.
Heat flows and harmonic maps with a free boundary.
Heat flows for extremal Kähler metrics
Let be a closed polarized complex manifold of Kähler type. Let be the maximal compact subgroup of the automorphism group of . On the space of Kähler metrics that are invariant under and represent the cohomology class , we define a flow equation whose critical points are the extremal metrics,i.e.those that minimize the square of the -norm of the scalar curvature. We prove that the dynamical system in this space of metrics defined by the said flow does not have periodic orbits, and that its...
Helmholtz conditions and their generalizations.
Hermitian harmonic maps.
Heteroclinic orbits for spatially periodic hamiltonian systems
Heteroclinic solutions to an asymptotically autonomous second-order equation.
Higher order graded and berezinian lagrangian densities and their Euler-Lagrange equations
Higher order Grassmann fibrations and the calculus of variations.
Higher-order phase transitions with line-tension effect
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.u is a scalar density function and...