We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if φ : M → N is a horizontally conformal map such that the tension field is divergence free, then φ is harmonic. Furthermore, if N is noncompact, then φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic...

In this note, we show that some F -harmonic maps into spheres are global maxima of the variations of their energy functional on the conformal group of the sphere. Our result extends partially those obtained in [15] and [17] for harmonic and p-harmonic maps.

According to Klein’s Erlangen program, different geometry branches study invariants of a space under different transformation groups. Topology and Euclidean geometry have been widely applied in computer graphics and vision. Between topological transformation group and Euclidean transformation group, there exists a conformal transformation group, which has not been well studied by computer scien...

Representation and comparison of shapes is a problem with many applications in computer vision and imaging, including object recognition and medical diagnosis. We will discuss some constructions from the theory of conformal mapping which provide ways to represent and compare planar shapes. It is a remarkable fact that conformal maps from the unit disk to a planar domain encode the geometry of t...

We present a novel approach to creating flat maps of the brain. Our approach attempts to preserve the conformal structure between the original cortical surface in 3-space and the flattened surface. We demonstrate this with data from the human cerebellum. Our maps exhibit quasiconformal behavior and offer several advantages over existing approaches.

We study the topology of a complete asymptotically hyperbolic Einstein manifold such that its conformal boundary has positive Yamabe invariant. We proved that all maps from such manifold into any nonpositively curved manifold are homotopically trivial. Our proof is based on a Bochner type argument on harmonic maps.

In this paper, we study Hölder-continuous linear cocycles over transitive Anosov diffeomorphisms. Under various conditions of relative pinching we establish properties including existence and continuity of measurable invariant subbundles and conformal structures. We use these results to obtain criteria for cocycles to be isometric or conformal in terms of their periodic data. We show that if th...

Designing cooling channels for the thermoplastic injection process is a very important step in mold design. A conformal cooling channel can significantly improve the efficiency and the quality of production in plastic injection molding. This paper introduces an approach to generate spiral channels for conformal cooling. The cooling channels designed by our algorithms has very simple connectivit...

We describe how conformal Minkowski, dSand AdS-spaces can be united into a single submanifold [N ] of RP . It is the set of generators of the null cone in M. Conformal transformations on the Mink-, dSand AdS-spaces are induced by O(2, 4) linear transformations on M. We also describe how Weyl transformations and conformal transformations can be resulted in on [N ]. In such a picture we give a de...

The AdS/CFT transformation relates two nonlinear realizations of (super)conformal groups: their realization in the appropriate field theories in Minkowski space with a Goldstone dilaton field and their realization as (super)isometry groups of AdS (super)spaces. It exists already at the classical level and maps the field variables and space-time coordinates of the given (super)conformal field th...