Restriction estimates using polynomial partitioning II
نویسندگان
چکیده
منابع مشابه
Distinct Distance Estimates and Low Degree Polynomial Partitioning
We give a shorter proof of a slightly weaker version of a theorem fromGuth and Katz (Ann Math 181:155–190, 2015): we prove that if L is a set of L lines in R3 with at most L1/2 lines in any low degree algebraic surface, then the number of r -rich points of L is L(3/2)+εr−2. This result is one of the main ingredients in the proof of the distinct distance estimate in Guth and Katz (2015). With ou...
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To see the issues that arise when studying incidence problems in higher dimensions, we consider one of the simplest cases: Incidences between m points and n planes in R. To see that this problem is not interesting, we consider the following point-plane configuration. Let l ⊂ R be a line, let P be a set of m points on l, and let H be a set of n planes that contain l (e.g., see Figure 1). This co...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2018
ISSN: 0001-5962,1871-2509
DOI: 10.4310/acta.2018.v221.n1.a3