photo

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. Euclidean Domains with Nearly Maximal Yamabe Quotient
              (with Xuan Yao)
  2. Mass, Conformal Capacity, and the Volumetric Penrose Inequality
              (with Xuan Yao)
  3. An Alternative for Constant Mean Curvature Hypersurfaces
              (with Xin Zhou)
  4. Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theory
              (with Xin Zhou)
  5. On the Stability of the Yamabe Invariant of S3
              (with Xuan Yao) Trans. Amer. Math. Soc., to appear
  6. Min-max Theory for Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
              (with Tongrui Wang)
  7. Curvature Estimates for Stable Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
              (with Tongrui Wang) Int. Math. Res. Not.
  8. Monotone Quantities for p-Harmonic Functions and the Sharp p-Penrose Inequality
              (with Xuan Yao) Math. Res. Lett., to appear
  9. The Yamabe Invariant of RP3 via Harmonic Functions
              (with Xuan Yao)
  10. The Half-Volume Spectrum of a Manifold
              (with Xin Zhou) Calc. Var. Partial Differential Equations, to appear
  11. Prescribed Mean Curvature Min-Max Theory in Some Non-Compact Manifolds
              Adv. Math.
  12. CMC Doublings of Minimal Surfaces via Min-Max
              J. Geom. Anal.
  13. A Weyl Law for the p-Laplacian
              J. Funct. Anal.

Recent Teaching