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A stationary set method for estimating oscillatory integrals

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arxiv 2103.08844 v3 pith:PYWHR7UR submitted 2021-03-16 math.CA math.AGmath.LOmath.NT

Saugata Basu , Shaoming Guo , Ruixiang Zhang , Pavel Zorin-Kranich This is my paper
classification math.CAmath.AGmath.LOmath.NT
keywords methodestimatingintegralsobtainoscillatorysharpstationarycall
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abstract

We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarry's problems in dimension two for every degree $k\ge 2$. As a consequence, we obtain sharp Fourier extension estimates for a family of monomial surfaces.

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  1. On restricted-type Strichartz estimates and the applications

    math.AP 2025-08 conditional novelty 6.0 of 10

    On waveguides, the shell-type Strichartz estimate is global and derivative-free on R2×T but must lose derivatives on R×T2, yielding first local well-posedness for the partially periodic Zakharov system.

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