65 citations · 177 across the 29 of their papers we have counts for
30 papers
Parabolic evolution with boundary to the Bishop family of holomorphic discs
Brendan Guilfoyle, Wilhelm Klingenberg
It is proven that a definite graphical rotationally symmetric line congruence evolving under mean curvature flow with respect to the neutral Kaehler metric in the space of oriented…
A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
Wilhelm Klingenberg, Ben Lambert, Julian Scheuer
Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike…
Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry
Samuël Borza, Wilhelm Klingenberg
We prove that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points. Namely that it does not behave like the injective map of reals gi…
Roots of Polynomials and Umbilics of Surfaces
Brendan Guilfoyle, Wilhelm Klingenberg
For certain polynomials we relate the number of roots inside the unit circle with the index of a non-degenerate isolated umbilic point on a real analytic surface in Euclidean 3-spa…
Regularity and Continuity properties of the sub-Riemannian exponential map
Samuël Borza, Wilhelm Klingenberg
We prove a version of Warner's regularity and continuity properties for the sub-Riemannian exponential map. The regularity property is established by considering sub-Riemannian Jac…
Proof of the Toponogov Conjecture on Complete Surfaces
Brendan Guilfoyle, Wilhelm Klingenberg
We prove a conjecture of Toponogov on complete convex planes, namely that such planes must contain an umbilic point, albeit at infinity. Our proof is indirect. It uses Fredholm reg…