INTERSECTION BETWEEN PENCILS OF TUBES, DISCRETIZED SUM-PRODUCT, AND RADIAL PROJECTIONS∗

Bochen Liu; Chun Yen Shen

doi:10.4310/AJM.2023.v27.n6.a1

INTERSECTION BETWEEN PENCILS OF TUBES, DISCRETIZED SUM-PRODUCT, AND RADIAL PROJECTIONS^∗

Bochen Liu
, Chun Yen Shen

Southern University of Science and Technology
National Taiwan University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove the following results in the plane. They are related other, while each of them has its own interest. First we obtain a nontrivial exponent on intersection between pencils of δ-tubes, undconcentration conditions. In fact we show it is equivalent to the discretized sum-product proThen we use our estimates of pencils to prove new results on dimensions of radial projeWe also make a conjecture that would reveal a key difference between orthogonal projectioradial projections.

Original language	English
Pages (from-to)	829-852
Number of pages	24
Journal	Asian Journal of Mathematics
Volume	27
Issue number	6
DOIs	https://doi.org/10.4310/AJM.2023.v27.n6.a1
State	Published - 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 International Press.

Keywords

discretized sum-product
pencil of tubes
radial projection
tube condition

Access to Document

10.4310/AJM.2023.v27.n6.a1

Cite this

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abstract = "In this paper we prove the following results in the plane. They are related other, while each of them has its own interest. First we obtain a nontrivial exponent on intersection between pencils of δ-tubes, undconcentration conditions. In fact we show it is equivalent to the discretized sum-product proThen we use our estimates of pencils to prove new results on dimensions of radial projeWe also make a conjecture that would reveal a key difference between orthogonal projectioradial projections.",

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KW - radial projection

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