Algebraic curves and non rigid minimal surfaces in the Euclidean space

Gian Pietro Pirola

Vol. 183 (1998), No. 2, 333–357

DOI: 10.2140/pjm.1998.183.333

Abstract

Using method from algebraic geometry we prove:

Theorem. Let X be a compact connected Riemann surface and Z be a non empty finite subset of X. Then there is a complete minimal immersion F : X − Z → ℝ³ such that F(X − Z) is non rigid and of finite total Gaussian curvature.

Milestones

Received: 10 April 1996

Revised: 9 April 1997

Published: 1 April 1998