By using Gromov’s $\mu$-bubble technique, we show that the $3$-dimensional spherical caps are rigid under perturbation that do not reduce the metric, the scalar curvature, and the mean curvature along its boundary. Several generalizations of this result will also be discussed. This talk is based on my recent joint work with my postdoc Y.H. Hu and my Ph.d. student P.Liu. The paper can be found on arXiv https://arxiv.org/abs/2205.08428