Abstract

The sweeping net method has been an effective tool for approximating singularities in two-dimensional manifolds. In this paper, we propose a conjecture that extends the sweeping net method to higher-dimensional manifolds with isolated singularities. We present a detailed formulation of the conjecture, discuss the key challenges in proving it, and explore potential approaches using local coordinate analysis, geometric measure theory, and multi-dimensional generalizations of trigonometric functions. This work aims to open new avenues in the study of singularities on manifolds and stimulate further research in this area.