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Resolvent estimate for asymptotically hyperbolic surfaces without evenness assumption

  • Wenzheng Wang
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Abstract

We prove a sharp cut-off resolvent estimate for the Laplacian on non-compact Riemannian manifolds whose ends satisfy the Cardoso--Vodev assumption and whose geometry near the trapped set agrees with that of an even asymptotically hyperbolic manifold with the corresponding resolvent estimate. As applications, we show the global Strichartz and spectral projection estimates on negatively curved asymptotically hyperbolic surfaces, without assuming the evenness at infinity.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026resolvent,
  title = {{Resolvent estimate for asymptotically hyperbolic surfaces without evenness assumption}},
  author = {Wenzheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14914},
  eprint = {2609.14914},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14914},
}
RIS
TY  - UNPB
TI  - Resolvent estimate for asymptotically hyperbolic surfaces without evenness assumption
AU  - Wenzheng Wang
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.14914
UR  - https://arxiv.org/abs/2609.14914
AB  - We prove a sharp cut-off resolvent estimate for the Laplacian on non-compact Riemannian manifolds whose ends satisfy the Cardoso--Vodev assumption and whose geometry near the trapped set agrees with that of an even asymptotically hyperbolic manifold with the corresponding resolvent estimate. As applications, we show the global Strichartz and spectral projection estimates on negatively curved asymptotically hyperbolic surfaces, without assuming the evenness at infinity.
ER  -