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Lorentzian Horospheres and Bartnik's Splitting Conjecture

by Dr. Carlos Vega of Saint Louis U

  • Geometry/ Topology Seminar
  • Topology Seminar
When Mon, Mar 16, 2015
from 04:10 PM to 05:00 PM
Where 200 Ritter Hall
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In the early 1980s, Yau posed the problem of establishing the rigidity of the classical singularity theorems of Hawking and Penrose. This led to a new school of Lorentzian splitting geometry, based on a direct transplant of the Riemannian Busemann function, and its level sets (horospheres). This transplant, however, suffers from poor regularity properties in the Lorentzian setting. Our work begins with a new, geometric approach to Lorentzian horospheres, which in particular, derives regularity in an elegant way from the causal structure. We introduce a new Cauchy horosphere, and use this to derive new results on Bartnik's splitting conjecture, a concrete realization of the problem posed by Yau. This is joint work with G. J. Galloway.
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