We consider Riemann mappings from bounded Lipschitz domains in the plane to a triangle. We show that in this case the Riemann mapping has a linear variational principle: it is the minimizer of the Dirichlet energy over an appropriate affine space. By discretizing the variational principle in a natural way we obtain discrete conformal maps which can be computed by solving a sparse linear system....

In this paper we introduce the fourth fundamental form for the hypersurfaces in H and the space-like hypersurfaces in S 1 and discuss the conformality of the normal Gauss maps of the hypersurfaces in H and S 1 . Particularly, we discuss the surfaces with conformal normal Gauss maps in H and S 1 and prove a duality property. We give the Weierstrass representation formula for the space-like surfa...

The locations and patterns of functional brain activity in humans are difficult to compare across subjects because of individual differences in cortical folding and the fact that 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 ...

The space of diffeomorphisms of the circle modulo boundary values of conformal maps of the disk. The Sobolev 3/2 norm on the tangent space space at id of the space of diffeomorphisms of the circle modulo boundary values of conformal maps of the disk induces the only Kähler left invariant metric defined up to a constant on the space of diffeomorphisms of the circle modulo boundary values of conf...

A conformal �attening maps a curved surface to the plane without distorting angles—such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing methods provide little direct control over the shape of the �attened domain, or else demand expensive nonlinear optimization. Boundary �rst �attening (BFF) is a line...