Liam Mazurowski

Office:	Malott 531
Email:	lmm334 [at] cornell [dot] edu

I am currently 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.

My research lies in Differential Geometry, Geometric Analysis, and PDEs with a focus on non-linear variational problems. In particular, I am interested in minimal surfaces, constant mean curvature surfaces, the p-Laplacian, and scalar curvature.

• Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theory
            (with Xin Zhou)
• On the Stability of the Yamabe Invariant of S³
            (with Xuan Yao)
• Min-max Theory for Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
            (with Tongrui Wang)
• Curvature Estimates for Stable Free Boundary Minimal Hypersurfaces in Locally Wedge-Shaped Manifolds
            (with Tongrui Wang) Int. Math. Res. Not., to appear
  
• Monotone Quantities for p-Harmonic Functions and The Sharp p-Penrose Inequality
            (with Xuan Yao) Math. Res. Lett., to appear
  
• The Yamabe Invariant of RP³ via Harmonic Functions
            (with Xuan Yao)
  
• The Half-Volume Spectrum of a Manifold
            (with Xin Zhou) Calc. Var. Partial Differential Equations, to appear
  
• Prescribed Mean Curvature Min-Max Theory in Some Non-Compact Manifolds
  
• CMC Doublings of Minimal Surfaces via Min-Max
            J. Geom. Anal.
• A Weyl Law for the p-Laplacian
  

• Spring 2024: Topics in PDE: The Allen-Cahn Equation
  
• Spring 2024: Introduction to Analysis
  
• Fall 2023: Measure Theory and Lebesgue Integration
  
• Spring 2023: Introduction to Analysis
  
• Fall 2022: Linear Algebra with Applications
  
• Spring 2022: Introduction to Analysis
  
• Fall 2021: Manifolds and Differential Forms (Lecture Notes)