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Local theory of wave equations with timelike curves of conic singularities

Peter Hintz

17/5/24 Published in : arXiv:2405.10669

We develop a general theory for the existence, uniqueness, and higher regularity of solutions to wave-type equations on Lorentzian manifolds with timelike curves of cone-type singularities. These singularities may be of geometric type (cone points with time-dependent cross sectional metric), of analytic type (such as asymptotically inverse square singularities or first order asymptotically scaling-critical singular terms), or any combination thereof. We can treat tensorial equations without any symmetry assumptions; we only require a condition of mode stability type for the stationary model operators defined at each point along the curve of cone points. In symmetric ultrastatic settings, we recover the solvability theory given by the functional calculus for the Friedrichs extension.

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Phase I & II research project(s)

  • Field Theory
  • Geometry, Topology and Physics

Phase III direction(s)

  • Differential equations of Mathematical Physics
  • From Field Theory to Geometry and Topology

Pairing Powers of Pythagorean Pairs

Irrational components of the Hilbert scheme of points

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The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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