Geometric Analysis and Topology Seminar

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Harmonic maps from the product of hyperbolic spaces to hyperbolic spaces

Speaker: Kazuo Akutagawa, Chuo University

Location: Warren Weaver Hall 512

Date: Friday, March 14, 2025, 11 a.m.

Synopsis:

In this talk, we will consider the asymptotic Dirichlet problem for harmonic maps from the product H^{m_1} x H^{m_2} of two hyperbolic spaces to hyperbolic spaces. It remarks that H^{m_1} x H^{m_2} is a higher rank symmetric space of noncompact type.

We first show uniqueness and non-existence results, particularly the existence of such harmonic maps (with some natural conditions) implies that it must be m _1 = m_2 = 2. We also show an existence result for harmonic maps from H^2 x H^2 to hyperbolic spaces.

This is a joint work with Yoshihiko Matsumoto.