Rigidity of 3D spherical caps viaμ-bubbles
Yuhao Hu, Peng Liu, Yuguang Shi
Abstract
By using Gromov's µ-bubble technique, we show that the 3-dimensional spherical caps are rigid under perturbations that do not reduce the metric, the scalar curvature, and the mean curvature along its boundary.Several generalizations of this result will be discussed.
Topics & Concepts
Rigidity (electromagnetism)MathematicsGeometryComposite materialMaterials scienceGeometric Analysis and Curvature FlowsPickering emulsions and particle stabilizationPoint processes and geometric inequalities