A necessary condition for the existence of a doubly connected minimal surface

作者：Lopez Rafael^*

来源：Annali di Matematica Pura ed Applicata, 2017, 196(4): 1513-1524.

DOI：10.1007/s10231-016-0626-z

• Minimal surface
• Riemann minimal example
• Elliptic integral

Given two circles contained in parallel planes, it is expectable that there does not exist a doubly connected minimal surface bounded by both circles if these circles are either laterally or vertically far away. In this paper, we give a quantitative estimate of this separation. We also obtain bounds for the height of a Riemann minimal example in terms of a catenoid with the same boundary radii and waist.

• 出版日期2017-8