## A restriction estimate using polynomial partitioning

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- by Larry Guth PDF
- J. Amer. Math. Soc.
**29**(2016), 371-413 Request permission

## Abstract:

If $S$ is a smooth compact surface in $\mathbb {R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\| E_S f\|_{L^p(\mathbb {R}^3)} \le C(p,S) \| f \|_{L^\infty (S)}$. The proof uses polynomial partitioning arguments from incidence geometry.## References

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## Additional Information

**Larry Guth**- Affiliation: Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
- MR Author ID: 786046
- Email: lguth@math.mit.edu
- Received by editor(s): July 14, 2014
- Received by editor(s) in revised form: January 23, 2015
- Published electronically: May 11, 2015
- Additional Notes: The author is supported by a Simons Investigator Award.
- © Copyright 2015 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**29**(2016), 371-413 - MSC (2010): Primary 42B20
- DOI: https://doi.org/10.1090/jams827
- MathSciNet review: 3454378