Determination of metrics by boundary energy.
Extremal properties of logarithmic spirals.
-harmonic maps which map the boundary of the domain to one point in the target.
Finite energy maps from Riemannian polyhedra to metric spaces.
First-order twistor lifts.
Formes harmoniques de longueur constante sur les variétés
From infinitesimal harmonic transformations to Ricci solitons
The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.
Gap properties of harmonic maps and submanifolds
In this article, we obtain a gap property of energy densities of harmonic maps from a closed Riemannian manifold to a Grassmannian and then, use it to Gaussian maps of some submanifolds to get a gap property of the second fundamental forms.
Generalized condensers and conformal properties of riemannian manifolds with at least two ends
Geometrical interpretation of solutions of certain PDEs.
Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces and
The exceptional compact symmetric spaces and admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.
Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
Harmonic conformal flows on manifolds of constant curvature
We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.
Harmonic functions on Riemannian manifolds with ends.
Harmonic maps and representations of non-uniform lattices of
We study representations of lattices of into . We show that if a representation is reductive and if is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic -space to complex hyperbolic -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into of non-uniform lattices in , and more generally of fundamental groups of orientable...
Harmonic maps and Riemannian submersions between manifolds endowed with special structures
It is well known that Riemannian submersions are of interest in physics, owing to their applications in the Yang-Mills theory, Kaluza-Klein theory, supergravity and superstring theories. In this paper we give a survey of harmonic maps and Riemannian submersions between manifolds equipped with certain geometrical structures such as almost Hermitian structures, contact structures, f-structures and quaternionic structures. We also present some new results concerning holomorphic maps and semi-Riemannian...
Harmonic maps and stability on -Kenmotsu manifolds.
Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces.
In this paper, we prove two Liouville theorems for harmonic maps and apply them to study the topology of manifolds with positive spectrum and stable minimal hypersurfaces in Riemannian manifolds with non-negative bi-Ricci curvature.
Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature
It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. If one reduces the assumption on the Ricci curvature to one on the scalar curvature, such a vanishing theorem does not hold in general. This raises the question: What information can we obtain from the existence of a non-constant harmonic map? This paper gives an answer to this problem when both manifolds are...
Harmonic metrics on four dimensional non-reductive homogeneous manifolds
We study harmonic metrics with respect to the class of invariant metrics on non-reductive homogeneous four dimensional manifolds. In particular, we consider harmonic lifted metrics with respect to the Sasaki lifts, horizontal lifts and complete lifts of the metrics under study.