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K-State Today

November 16, 2017

Mathematics Colloquium lecture Nov. 16

Submitted by Reta McDermott

Yuxin Dong, Fudan University, will present "On Eells-Sampson Type Theorems for Subelliptic Harmonic Maps" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, Nov. 16, in 122 Cardwell Hall.

A sub-Riemannian manifold is a manifold with a subbundle of the tangent bundle and a fiber metric on this subbundle. A Riemannian extension of a sub-Riemannian manifold is a Riemannian metric on the manifold compatible with the fiber metric on the subbundle. One may define an analogue of the Dirichlet energy by replacing the L2 norm of the derivative of a map between two manifolds with the L2 norm of the restriction of the derivative to the subbundle when the domain is a sub-Riemannian manifold. A critical map for this energy is called a subelliptic harmonic map.

In this talk, by use of a subelliptic heat flow, we establish some Eells-Sampson type existence results for subelliptic harmonic maps when the target Riemannian manifold has nonpositive sectional curvature.