[geometry-ml:05074] 学習院・早稲田幾何学セミナー 3/13 14:00- @目白

[Sumio Yamada]

みなさま、

以下の通り、対面のセミナーを行います。
https://pc1.math.gakushuin.ac.jp/~hosono/GWGS/GWGS.html

ご興味のある方は、是非ご参加ください。

山田澄生

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2023年3月13日（月）14:00～15:30
講演者： Gilbert Weintein (Ariel University)

題目: Asymptotic Analysis of Harmonic Maps with Prescribed Singularities
於：学習院大学 南1号館103教室

概要：Motivated by stationary axially symmetric solutions of the Einstein
field equations, we study harmonic maps with prescribed singularities from
domains in 3-d Euclidean space into the hyperbolic plane. The boundary
conditions require these to be singular near the z-axis and asymptotic to
extreme Kerr harmonic maps near punctures on the z-axis, corresponding to
degenerate event horizons. It is proven that every such map admits a unique
tangent map at each such puncture. The possible tangent maps are classified
and shown to be maps into geodesics in the hyperbolic plane, depending on
two parameters, angular momentum and conical singularity. The rate of
convergence to the tangent map is established. A similar expansion is also
obtained at the asymptotically flat end. Together with earlier results,
this provides a complete regularity theory for these harmonic maps with
prescribed singularities. These results are in preparation of a study of
the mass-angular-momentum inequality for  axially symmetric vacuum data
with multiple black holes.

This is joint work with Marcus Khuri, Qing Han, and Jingang Xiong.

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