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Liam Mazurowski

Office: Chandler-Ullmann 222
Email: lim624 [at] lehigh [dot] edu

About

I am currently a C.C. Hsiung Postdoctoral Research Associate at Lehigh University. Prior to that, I was an H.C. Wang Assistant Professor at Cornell University mentored by Xin Zhou. I received my PhD from the University of Chicago in June 2021. My advisor was André Neves.

Research

My research lies in differential geometry, geometric analysis, and PDEs. I am especially interested in prescribed mean curvature surfaces, scalar curvature, and the p-Laplacian.

  1. A Positive Mass Theorem for Continuous Metrics
              (with Xuan Yao)
  2. Scalar Curvature under Weak Limits of Manifolds
              (with Xuan Yao)
  3. Quantification of C0 Convergence in Dimension Three
              (with Xuan Yao)
  4. Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature
              (with Xin Zhou)
  5. On the Topology of Manifolds with Positive Intermediate Curvature
              (with Tongrui Wang and Xuan Yao) Advances in Mathematics
  6. Existence of Constant Mean Curvature Surfaces in Asymptotically Flat and Asymptotically Hyperbolic Manifolds
              (with Jintian Zhu)
  7. Euclidean Domains with Nearly Maximal Yamabe Quotient
              (with Xuan Yao)
  8. Mass, Conformal Capacity, and the Volumetric Penrose Inequality
              (with Xuan Yao) Communications in Analysis and Geometry
  9. An Alternative for Constant Mean Curvature Hypersurfaces
              (with Xin Zhou) Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, to appear
  10. Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theory
              (with Xin Zhou)
  11. On the Stability of the Yamabe Invariant of S3
              (with Xuan Yao) Transactions of the American Mathematical Society, to appear
  12. Min-max Theory for Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
              (with Tongrui Wang)
  13. Curvature Estimates for Stable Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
              (with Tongrui Wang) International Mathematics Research Notices
  14. Monotone Quantities for p-Harmonic Functions and the Sharp p-Penrose Inequality
              (with Xuan Yao) Mathematical Research Letters
  15. The Yamabe Invariant of RP3 via Harmonic Functions
              (with Xuan Yao)
  16. The Half-Volume Spectrum of a Manifold
              (with Xin Zhou) Calculus of Variations and Partial Differential Equations
  17. Prescribed Mean Curvature Min-Max Theory in Some Non-Compact Manifolds
              Advances in Mathematics
  18. CMC Doublings of Minimal Surfaces via Min-Max
              Journal of Geometric Analysis
  19. A Weyl Law for the p-Laplacian
              Journal of Functional Analysis

Recent Teaching