Related papers: Biharmonic submanifolds into ellipsoids
We give some general results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space. These results are mainly concerned with submanifolds with constant mean curvature or parallel mean…
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely…
We construct bi-Lipschitz embeddings into Euclidean space for manifolds and orbifolds of bounded diameter and curvature. The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. Our results also…
In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.
We prove several unique continuation results for biharmonic maps between Riemannian manifolds.
Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we…
We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds.
In this note, we classify biharmonic submanifolds in a sphere defined by bi-eigenmaps ($\Delta^2 \phi=\lambda \phi$) or buckling eigenmaps ($\Delta^2 \phi=-\mu \Delta \phi$). We then classify biharmonic bi-eigenmaps and buckling eigenmaps…
We study f-biharmonic and bi-f-harmonic submanifolds in both generalized complex and Sasakian space forms. We prove necessary and sufficient condition for f-biharmonicity and bi-f-harmonicity in the general case and many particular cases.…
In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded…
An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic…
The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…
In this note we prove a Weierstrass representation formula for pluriminimal submanifolds of euclidean spaces. We use this formula to produce new families of examples of pluriminimal submanifolds. We also prove that any affine algebraic…
We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.
We classify the space-like biharmonic surfaces in 3-dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.
We give a geometric condition on a compact subset of a complex manifold which is necessary and sufficient for the existence of a smooth strictly plurisubharmonic function defined in a neighbourhood of this set.
In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy many of their important properties.…