Following Gromov, a Riemannian manifold is called "area extremal" if any modification of which increases scalar curvature must decrease the area of a 2-plane. Previous work of Llarull and Goette-Semmelmann has established area extremality for certain metrics with nonnegative curvature operator, and Kahler metrics with positive Ricci curvature. We show that in dimension 4 a larger class of nonnegatively curved metrics are area extremal, including on manifolds which do not admit metrics with nonnegative curvature operator or Kahler metrics. Following Lott, we examine area extremality on 4-manifolds with boundary, proving that all positively curved metrics are "locally" area extremal.
Geometry-Topology Seminar
Thursday, March 24, 2022 - 5:15pm
Jackson Goodman
Berkeley
Other Events on This Day
There are no other events scheduled for this day.