On the interaction of metric trapping and a boundary

Kiril Datchev, Jason Metcalfe, Jacob Shapiro, Mihai Tohaneanu

Research output: Contribution to journalArticlepeer-review


By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as the boundary passes through the trapped set, one goes from a nontrapping scenario where lossless local energy estimates are available for the wave equation to the case of stably trapped rays where all but a logarithmic amount of decay is lost.

Original languageEnglish
Pages (from-to)3801-3812
Number of pages12
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - 2021

Bibliographical note

Funding Information:
Received by the editors August 13, 2020, and, in revised form, December 1, 2020. 2020 Mathematics Subject Classification. Primary 35R01; Secondary 35B45. The first author was supported in part by NSF grant DMS-1708511, the third author was supported in part by the Australian Research Council through grant DP180100589, and the fourth author was supported in part by Simons Collaboration Grant 586051.

Publisher Copyright:
© 2021 American Mathematical Society

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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