TY - JOUR

T1 - Constant mean curvature surfaces based on fundamental quadrilaterals

AU - Bobenko, Alexander I.

AU - Heller, Sebastian

AU - Schmitt, Nicholas

N1 - Funding Information: The first author is partially supported by the DFG Collaborative Research Center TRR 109 Discretization in Geometry and Dynamics. The second author is supported by the DFG grant HE 6829/3-1 of the DFG priority program SPP 2026 Geometry at Infinity. The third author is supported by the DFG Collaborative Research Center TRR 109 Discretization in Geometry and Dynamics.

PY - 2021/11/6

Y1 - 2021/11/6

N2 - We describe the construction of CMC surfaces with symmetries in \(\mathbb S^3\) and \(\mathbb R^3\) using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the space. The fundamental piece is constructed by the generalized Weierstrass representation using a geometric flow on the space of potentials.

AB - We describe the construction of CMC surfaces with symmetries in \(\mathbb S^3\) and \(\mathbb R^3\) using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the space. The fundamental piece is constructed by the generalized Weierstrass representation using a geometric flow on the space of potentials.

KW - math.DG

KW - Tesselations

KW - Flat connections

KW - CMC surface

KW - DPW method

UR - http://www.scopus.com/inward/record.url?scp=85118746742&partnerID=8YFLogxK

U2 - 10.1007/s11040-021-09397-z

DO - 10.1007/s11040-021-09397-z

M3 - Article

VL - 24

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

SN - 1385-0172

IS - 4

M1 - 37

ER -