Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"Isometric immersions which are minimal with respect to special variations of ambient metric"
Let L be a fixed compact oriented submanifold of a manifold M. Consider the volume functional of L with respect to variations of an ambient Riemannian metric on M. It is easy to show that with respect to general variations, there are no critical points. However, if (M, g) has additional extra structure, then with respect to a particular special class of metric variations, there can be critical points. I will discuss a result of Arezzo-Sun in this context concerning complex submanifolds of a Kahler manifold. In ongoing work with Daren Cheng and Jesse Madnick, we have generalized this result to both the non-integrable setting and to G2-structures. Surprisingly, the Spin(7) analogue is false.
Zoom meeting: https://zoom.us/j/93324862932?pwd=dUdCMGJZL1A3UTBpOXVYNVROdHpKUT09