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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. 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 with a focus on non-linear variational problems. In particular, I am interested in prescribed mean curvature surfaces, scalar curvature, and the p-Laplacian.

  1. Mass, Conformal Capacity, and the Volumetric Penrose Inequality
              (with Xuan Yao)
  2. An Alternative for Constant Mean Curvature Hypersurfaces
              (with Xin Zhou)
  3. Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theory
              (with Xin Zhou)
  4. On the Stability of the Yamabe Invariant of S3
              (with Xuan Yao)
  5. Min-max Theory for Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
              (with Tongrui Wang)
  6. Curvature Estimates for Stable Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
              (with Tongrui Wang) Int. Math. Res. Not.
  7. Monotone Quantities for p-Harmonic Functions and the Sharp p-Penrose Inequality
              (with Xuan Yao) Math. Res. Lett., to appear
  8. The Yamabe Invariant of RP3 via Harmonic Functions
              (with Xuan Yao)
  9. The Half-Volume Spectrum of a Manifold
              (with Xin Zhou) Calc. Var. Partial Differential Equations, to appear
  10. Prescribed Mean Curvature Min-Max Theory in Some Non-Compact Manifolds

  11. CMC Doublings of Minimal Surfaces via Min-Max
              J. Geom. Anal.
  12. A Weyl Law for the p-Laplacian
              J. Funct. Anal.

Recent Teaching