Related papers: Biharmonic functions on the classical compact simp…

We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic…

We study the problem of classifying the holomorphic $(m,n)$-subharmonic morphisms in complex space. This determines which holomorphic mappings preserves $m$-subharmonicity in the sense that the composition of the holomorphic mapping with a…

Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…

We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an…

Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The…

In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal…

In this article, we introduce the concept of normal families of bicomplex holomorphic functions to obtain a bicomplex Montel theorem. Moreover, we give a general definition of Fatou and Julia sets for bicomplex polynomials and we obtain a…

In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to…

Motivated by the rich theory of harmonic maps from a 2-sphere, we study biharmonic maps from a 2-sphere in this paper. We first derive biharmonic equation for rotationally symmetric maps between rotationally symmetric 2-manifolds. We then…

We propose a generalization of the so-called rational map ansatz on the Euclidean space $\mathbb{R}^3$, for any compact simple Lie group $G$ such that $G/{\widehat K}\otimes U(1)$ is an Hermitian symmetric space, for some subgroup…

We construct a new class of biharmonic maps, which are the critical points for the bienergy functional, by deforming conformally the codomain metric of harmonic Riemannian submersions such that they become nonharmonic but biharmonic.

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…

We generalize the Ruh-Vilms problem by characterizing the submanifolds in Euclidean spaces with proper biharmonic Gauss map and we construct examples of such hypersurfaces.

We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…

We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with…

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…

We study the holomorphic/meromorphic function theory and the fundamental group of Euclidean open neighborhoods of compact subvarieties in homogeneous spaces; building on results of Hironaka, Hartshorne, Napier and Ramachandran in the ample…

In this work we construct new multidimensional families of complete minimal submanifolds, of the classical non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(2n)/U(n) and SU*(2n)/Sp(n), of codimension two.

In this paper, we give a necessarly and sufficient condition for orbits of linear isotropy representations of Riemannian symmetric spaces are biharmonic submanifolds in hyperspheres in Euclidean spaces. In particular, we obtain examples of…