Matthew J. Hirn

Learn More
In this paper we consider a wide class of generalized Lipschitz extension problems and the corresponding problem of finding absolutely minimal Lipschitz extensions. We prove that if a minimal Lipschitz extension exists, then under certain other mild conditions, a quasi absolutely minimal Lipschitz extension must exist as well. Here we use the qualifier "(More)
Harmonic frames of prime order are investigated. The primary focus is the enumeration of inequivalent harmonic frames, with the exact number given by a recursive formula. The key to this result is a one-to-one correspondence developed between inequivalent harmonic frames and the orbits of a particular set. Secondarily, the symmetry group of prime order(More)
We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R d , a function f : E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C 1,1 (R d) with the minimum possible value of Lip(∇F). We present practical, efficient algorithms for constructing an F such(More)
  • 1