Abstract

When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show that the set of admissible variations can be widened in a geometrically meaningful manner leading to a more general notion of index. This allows us to produce explicit examples of destabilizing perturbations for the fundamental Scherk surface. For the dihedral Enneper surfaces we show that both the classical and modified index can be explicitly determined.

中文翻译：

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数值不稳定的最小圆盘

摘要

在计算最小曲面的索引时，具有紧支撑的域上的光滑函数集是描述容许变化的标准设置。我们表明，可以以几何上有意义的方式扩大允许变化的集合，从而产生更一般的索引概念。这使我们能够为基本的 Scherk 表面生成不稳定扰动的明确示例。对于二面体 Enneper 曲面，我们表明经典和修正指数都可以明确确定。