Stephen E. McKeown

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Research

I study, broadly, differential geometry, geometric analysis, and PDEs. I am particularly interested in the geometry of submanifolds in conformal geometry, and in related questions in geometric PDEs on singular domains (such as domains with corners). I am interested in connections of all these subjects to physics, especially via the AdS/CFT correspondence. I have various ongoing projects that are suitable for participation by graduate students or undergraduates.

Here is a current list of my published and submitted papers. I am preparing several more.

  1. (With Matthew J. Gursky and Aaron J. Tyrrell) Self-dual and even Poincaré-Einstein metrics (submitted)
  2. (With Jeffrey S. Case, Yueh-Ju Lin, Cheikh Birahim Ndiaye, and Paul Yang) A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball (submitted)
  3. (With Matthew J. Gursky and Aaron J. Tyrrell) "Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces" (arXiv); Advances in Theoretical and Mathematical Physics 26(9), 3081-3123 (2022).
  4. (With Sun-Yung Alice Chang and Paul Yang) "Scattering on singular Yamabe spaces"(arXiv); Revista Matemática Iberoamericana 38 (7), 2153-2184 (2022)
  5. "Extrinsic curvature and conformal Gauss-Bonnet for four-manifolds with corner" (arXiv); Pacific Journal of Mathematics 314(2), 411-424 (2021)
  6. "Formal theory of cornered asymptotically hyperbolic Einstein metrics" (arXiv); Journal of Geometric Analysis 29(3), 1876-1928 (2019).
  7. "Exponential map and normal form for cornered asymptotically hyperbolic metric" (arXiv); Transactions of the AMS 372, 4391-4424 (2019).