Isoperimetric Type Inequalities and Hypersurface Flows (Journal of Mathematical Study, 2021)
New types of hypersurface flows have been introduced recently with goalsto establish isoperimetric type inequalities in geometry. These flows serve as efficientpaths to achieve the optimal solutions to the problems of calculus of variations in geometric setting. The main idea is to use variational structures to develop hypersurfaceflows which are monotonic for the corresponding curvature integrals (including volume and surface area). These new geometric flows pose interesting but challengingPDE problems. Resolution of these problems have significant geometric implications.