In this talk, we will continue to discuss the isoperimetric surface technique that was developed by Professor Hubert Bray in his PhD thesis. This time, we are going to study the effect of non-negativity of scalar curvature on a complete asymptotically flat three-manifold. In particular, we will use the isoperimetric surface technique to prove two conditional Penrose inequality for single/multiple horizons cases. In contrast to last time, we are dealing with a minimizing process in non-compact manifolds, so we need to address the existence of area minimizers with its volume constraint. References: [H. Bray, PhD thesis](https://arxiv.org/abs/0902.3241), [Guide to Boundary Value Problems for Dirac-Type Operators](https://arxiv.org/abs/2301.05087)
