23 citations · 39 across the 8 of their papers we have counts for
8 papers
Periodic networks of fixed degree minimizing length
Jerome Alex, Karsten Grosse-Brauckmann
We study networks in which are periodic under a lattice of rank~ and have vertices of prescribed degree . We minimize the length of the quotient networks, subject…
Construction of embedded periodic surfaces in
Karsten Grosse-Brauckmann, Susanne Kürsten
We construct embedded minimal surfaces which are -periodic in . They are new for codimension . We start with a Jordan curve of edges of the -dimension…
Periodic Steiner networks minimizing length
Jerome Alex, Karsten Grosse-Brauckmann
We study a problem of geometric graph theory: We determine the triply periodic graph in Euclidean 3-space which minimizes length among all graphs spanning a fundamental domain of 3…
Coplanar k-unduloids are nondegenerate
Karsten Grosse-Brauckmann, Nicholas J. Korevaar, Robert B. Kusner +2
We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there is no nontrivial square-int…
Coplanar constant mean curvature surfaces
Karsten Grosse-Brauckmann, Robert B. Kusner, John M. Sullivan
We consider constant mean curvature surfaces of finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were cons…
Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero
Karsten Grosse-Brauckmann, Robert B Kusner, John M Sullivan
In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC…