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 construct a solution of the classical equations of motion arising in the low energy effective field theory for heterotic string theory. This solution describes a black hole in four dimensions carrying mass M , charge Q and angular momentum J . The extremal limit of the solution is discussed.

We study the regularity of the extremal solution of the semilinear biharmonic equation ∆u = λ (1−u)2 , which models a simple Micro-Electromechanical System (MEMS) device on a ball B ⊂ R , under Dirichlet boundary conditions u = ∂νu = 0 on ∂B. We complete here the results of F.H. Lin and Y.S. Yang [14] regarding the identification of a “pull-in voltage” λ∗ > 0 such that a stable classical soluti...

We study the regularity of the extremal solution of the semilinear biharmonic equation ∆u = λ (1−u)2 , which models a simple Micro-Electromechanical System (MEMS) device on a ball B ⊂ R , under Dirichlet boundary conditions u = ∂νu = 0 on ∂B. We complete here the results of F.H. Lin and Y.S. Yang [14] regarding the identification of a “pull-in voltage” λ > 0 such that a stable classical solutio...

The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes a...

The picture of S-wave scattering from a 4D extremal dilatonic black hole is examined. Classically, a small matter shock wave will form a non-extremal black hole. In the “throat region” the r − t geometry is exactly that of a collapsing 2D black hole. The 4D Hawking radiation (in this classical background) gives the 2D Hawking radiation exactly in the throat region. Inclusion of the back-reactio...

We present a static multi-center magnetic solution of toroidally compactified heterotic string theory, which is T-duality covariant. The space-time geometry depends on the mass M and on the O(6,22)-norm N of the magnetic charges. For different range of parameters (M,N)-solution includes 1) two independent positive parameters extremal magnetic black holes with non-singular geometry in stringy fr...