Abstract: Despite being the weakest among notions of curvature, scalar curvature exhibits several rigidity properties, for instance, the positive mass theorem, the Geroch conjecture, and the more recent Gromov dihedral rigidity. In 1998, Llarull established a rigidity result for metrics on the round sphere under scalar curvature and metric comparison.

In this talk, we report on recent progress toward understanding scalar curvature rigid domains in warped product, where the warping function satisfies a log-concavity condition. Our main analytical tools are stable prescribed mean curvature surfaces with varying boundary contact angles, also known as stable capillary mu-bubbles. Particular emphasis will be placed on the role of tangent cone analysis in the presence of point singularities on the boundary, where additional technical challenges arise.

This is joint work with Gaoming Wang (YMSC).

Biography: He received his Ph.D. from the Chinese University of Hong Kong in 2018 and subsequently held postdoctoral positions at the Korea Institute for Advanced Study (KIAS). He is currently a BK21 Research Fellow at Pohang University of Science and Technology (POSTECH). His research interests lie in the areas of minimal surfaces, mean curvature flow, and scalar curvature.

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