R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Sweeping out minimal cones in Euclidean space
Hojoo Lee (Seoul National University)
In 1867, Riemann discovered a family of embedded, singly periodic, minimal surfaces (in the three dimensional Euclidean space) foliated by circles and lines. He also proved that his staircases, planes, catenoids, and helicoids are the only minimal surfaces fibered by circles or lines in parallel planes.
We explicitly construct generalized helicoids in odd dimensional Euclidean space, and minimal cones in even dimensional Euclidean space. Our minimal varieties unify various interesting examples: helicoids foliated by straight lines, Choe-Hoppe’s minimal hypersurfaces foliated by Clifford cones, Barbosa-Dajczer-Jorge’s ruled minimal submanifolds, and Harvey-Lawson’s twisted normal cone over Clifford torus.
This is joint work with Eunjoo Lee.
