This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

Conformal maps are widely used in geometry processing applications. They are smooth, preserve angles, and are locally injective by construction. However, conformal maps do not allow for boundary positions to be prescribed. A natural extension to the space of conformal maps is the richer space of quasiconformal maps of bounded conformal distortion. Extremal quasiconformal maps, that is, maps min...

We consider the problem of constructing quasi-conformal mappings between surfaces by solving Beltrami equations. This is of great importance for shape registration. In the physical world, most surface deformations can be rigorously modeled as quasi-conformal maps. The local deformation is characterized by a complex-value function, Beltrami coefficient, which describes the deviation from conform...

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by balls to quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated groups. Inspired work Benjamini and Schramm, we show under such maps, some kind of dimension increases: exponent volume growth nilpotent groups, the ideal boundary hyperbo...

We discuss a numerical implementation of conformal welding for finitely connected regions using the geodesic zipper algorithm and Koebe’s iterative method for computing conformal maps to regions bounded by circles. We also show that a conformal map from a finitely connected region to a region bounded by circles can be written as a composition of finitely many conformal maps of simply connected ...

Comparing the location and size of functional brain activity across subjects is difficult due to individual differences in folding patterns and functional foci are often buried within cortical sulci. Cortical flat mapping is a tool which can address these problems by taking advantage of the two-dimensional sheet topology of the cortical surface. Flat mappings of the cortex assist in simplifying...