## Downloadables

**Notes and slides**

*Some notes on geometric notion of derivatives* PDF

Some very rough and unpolished notes summarizing some things that are quite well-known to the experts. May be helpful to those just gaining proficiency in differential geometry. This may be updated to be something more serious later.

*Stability of de Sitter space under the Lorentzian constant mean curvature flow* Prezi

On November 3, 2014, I will gave the GAPDE seminar at DPMMS. For this talk I decided to try something different and use a Prezi. Overall I think it went well.

*Small data shock formation for QNLW* PDF

On January 13 and 14, 2014, Gustav Holzegel and I gave a minicourse at the OXPDE Workshop on Nonlinear Waves and General Relativity, on the subject of small data shock formation for quasilinear wave equations. These are the slides.

*Introductory notes on Sobolev spaces* PDF

I gave a few introductory lectures on Sobolev spaces for the Cambridge Center for Analysis course on PDEs taught by Mihalis Dafermos in spring of 2011.

*How to derive the Kerr metric by cheating quite a bit* PDF

This came from a lecture I gave to MAT 451 at Princeton University on April 23, 2009. MAT 451 is a senior level mathematics course in which the instructor has great leeway in deciding what to teach. In 2009 my thesis advisor was in charge, and focused the discussion on mathematical aspects of general relativity. In this note I showed how one can start from the Schwarzschild metric, make an educated guess on an algebraic structure, and arrive at the Kerr metric.

**Research papers**

*(Below is generated automatically from my arXiv.org author profile; they are sorted in order of most recent updates. Since I deposit all my research articles on the arXiv, the above link can give a slightly more pleasing browsing experience.)*

- Warped Product Space-times Xinliang An, Willie Wai Yeung Wong
- A commuting-vector-field approach to some dispersive estimates Willie Wai Yeung Wong
- Stable shock formation for nearly simple outgoing plane symmetric waves Jared Speck, Gustav Holzegel, Jonathan Luk, Willie Wong
- Singularities of axially symmetric time-like minimal submanifolds in Minkowski space Willie Wai-Yeung Wong
- Global Existence for the Minimal Surface Equation on $\mathbb{R}^{1,1}$ Willie Wai Yeung Wong
- Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space Roland Donninger, Joachim Krieger, Jeremie Szeftel, Willie Wong
- Stability and instability of expanding solutions to the Lorentzian constant-positive-mean-curvature flow Willie Wai-Yeung Wong
- Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An Overview Gustav Holzegel, Sergiu Klainerman, Jared Speck, Willie Wong
- A comment on the construction of the maximal globally hyperbolic Cauchy development Willie Wai-Yeung Wong
- On type I blow up formation for the critical NLW Joachim Krieger, Willie Wong
- Non-existence of multiple-black-hole solutions close to Kerr-Newman Willie Wai-Yeung Wong, Pin Yu
- A positive mass theorem for two spatial dimensions Willie Wai-Yeung Wong
- Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps Willie Wai-Yeung Wong
- Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria G. W. Gibbons, C. M. Warnick, W. W. Wong
- Dominant energy condition and causality for Skyrme-like generalizations of the wave-map equation Willie Wai-Yeung Wong
- On strong unique continuation of coupled Einstein metrics Willie Wai-Yeung Wong, Pin Yu
- A space-time characterization of the Kerr-Newman metric Willie Wai-Yeung Wong

[…] Notes and slides […]