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<p>We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and spectral projection estimates on manifolds of uniformly bounded geometry with nonpositive and negative sectional curvatures, extending the recent works of the first two authors for compact manifolds. We are able to use these along with known <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation>-local smoothing and new <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> <mo stretchy="false">→</mo> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2} \to L^{q}$</EquationSource> </InlineEquation> half-localized resolvent estimates to obtain our lossless bounds.</p>

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Lossless Strichartz and Spectral Projection Estimates on Unbounded Manifolds

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Xiaoqi Huang,
  • Christopher D. Sogge,
  • Zhongkai Tao,
  • Zhexing Zhang

摘要

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and spectral projection estimates on manifolds of uniformly bounded geometry with nonpositive and negative sectional curvatures, extending the recent works of the first two authors for compact manifolds. We are able to use these along with known L 2 $L^{2}$ -local smoothing and new L 2 → L q $L^{2} \to L^{q}$ half-localized resolvent estimates to obtain our lossless bounds.