Ryan Unger

Department of Mathematics, Stanford University
Building 380, Stanford, CA 94305
Office 384-E
email: runger [at] stanford [dot] edu

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I'm an NSF Postdoc at Stanford University, hosted by Jonathan Luk, and a Miller Fellow at UC Berkeley, hosted by Sung-Jin Oh.
I'm interested in general relativity, nonlinear wave equations, and geometric analysis.
Here is my CV (updated 07/14/24).

I received my PhD at Princeton University in 2024, where I was advised by Mihalis Dafermos.
I received my undergraduate degree at the University of Tennessee, where I was mentored by Alexandre Freire.

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Papers

1. Nonlinear stability of extremal Reissner–Nordström black holes in spherical symmetry (2024)
   with Yannis Angelopoulos and Christoph Kehle
   arXiv:2410.16234
   the arXiv version has bugged figures which have been fixed here

2. A note on Huisken's isoperimetric mass (2024)
   with Jeff Jauregui and Dan A. Lee
   to appear in Lett. Math. Phys. (arXiv:2408.08871)

3. Extremal black hole formation as a critical phenomenon (2024)
   with Christoph Kehle
   arXiv:2402.10190

4. Event horizon gluing and black hole formation in vacuum: the very slowly rotating case (2023)
   with Christoph Kehle
   Advances in Mathematics 452 (2024) (arXiv:2304.08455)

5. Gravitational collapse to extremal black holes and the third law of black hole thermodynamics (2022)
   with Christoph Kehle
   to appear in J. Eur. Math. Soc. (arXiv:2211.15742)

6. Noncompact fill-ins of Bartnik data (2022)
   with Dan A. Lee and Martin Lesourd
   J. Geom. Anal. 34:102 (2024) (arXiv:2211.06280)

7. Density and positive mass theorems for incomplete manifolds (2022)
   with Dan A. Lee and Martin Lesourd
   Calc. Var. Partial Differential Equations 62 (2023) (arXiv:2201.01328)

8. Density and positive mass theorems for initial data sets with boundary (2021)
   with Dan A. Lee and Martin Lesourd
   Comm. Math. Phys. 395.2 (2022) (arXiv:2112.12017)

9. The positive mass theorem with arbitrary ends (2021)
   with Martin Lesourd and Shing-Tung Yau
   J. Differential Geom. 128.1 (2024) (arXiv:2103.02744)

10. Positive scalar curvature on noncompact manifolds and the Liouville theorem (2020)
    with Martin Lesourd and Shing-Tung Yau
    to appear in Comm. Anal. Geom. (arXiv:2009.12618)

Talks

Miscellaneous