4-8【Peng Wang】On Willmore problem for surfaces and submanifolds in spheres

In this talk we will report our recent works on the Willmore problem for surfaces and submanifolds in spheres. For the case of surfaces, we will introduce the classification of Willmore two-spheres, characterization of Clifford torus and Lawson's embedded minimal surface \xi_{𝑚,𝑘}. For submanifolds, we will show the construction of \lambda_1 minimal flat 3-tori and 4-tori in spheres. We will also consider the index of minimal submanifolds in spheres as well as Willmore stability of some minimal submanifolds.