4 papers
The Bishop family of holomorphic discs: regularity and higher index
Brendan Guilfoyle, Wilhelm Klingenberg
We prove -regularity up to a non-umbilic elliptic complex point for the Bishop family of holomorphic discs with boundary in a regular real surface. Furtherm…
Smirnov Decomposition of a Horizontal Vector Charge in the Heisenberg Group
Zhengyao Huang, Wilhelm Klingenberg
A divergence-free horizontal vector current in Heisenberg space may be viewed as an element of the dual space of horizontal test vector fields. By applying a horizontal Liouville t…
The three obdurate conjectures of differential geometry
Brendan Guilfoyle, Wilhelm Klingenberg
We explore the role of symmetry in three obdurate conjectures of differential geometry: the Carathéodory, the Willmore and the Lawson Conjectures. All three Conjectures concern su…
Optimal transport on the sub-Lorentzian Heisenberg group
Samuël Borza, Wilhelm Klingenberg, Patrick Wood
We investigate the synthetic metric spacetime structure of the sub-Lorentzian Heisenberg group and we study the optimal transport problem in this space. The sub-Lorentzian version…