Xuan Yao （姚萱）

Education and Positions

Education and Positions

[ 08/2017 ] - [ 06/2021 ]

[ Institution ] Tsinghua University

[ Degree ] Bachelor of Science

[ 08/2021 ] - [ 05/2025 ]

[ Institution ] Cornell University

[ Program ] Mathematics

[ Degree ] Doctor of Philosophy

My PhD. advisor is Xin Zhou.

[09/2025] - [08/2026]

[Institution] Princeton University

[Position] Postdoctoral Research Associate

My mentor at Princeton is Sun-Yung Alice Chang.

[09/2026]-Now

[Institution] University of Chicago

[Position] Dickson Instructor

My research mentor at U Chicago is André Neves

“Whatever it is you're seeking won't come in the form you're expecting.” ― Haruki Marakami

Research

My research interests lie in Scalar curvatures, Yamabe Invariants, Mathematical Relativity and Minimal Surfaces.

Here are my works on Positive curvature:

A Positive Mass Theorem for Continuous Metrics. joint with Liam Mazurowski (06/2026)

Rigidity in the positive mass theorem with $C^0$ decay. joint with Liam Mazurowski (05/2026)

Scalar curvature under weak limits of manifolds. joint with Liam Mazurowski (05/2026)

Quantification of $C^0$ convergence in dimension 3. joint with Liam Mazurowski (04/2026)

Capillary minimal slicing and scalar curvature rigidity joint with Dongyeong Ko (02/2026)

On the topology of manifolds with positive intermediate curvature. joint with Liam Mazurowski and Tongrui Wang (03/2025) , to appear in Adv. Math.

A Note on Scalar curvature comparison rigidity for compact domains. (10/2024)

Scalar curvature comparison and rigidity of 3-dimensional weakly convex domains. joint with Dongyeong Ko (10/2024)

Generalized S^1 stability theorem. joint with Tongrui Wang (09/2023), to appear in Journal of Topology and Analysis.

Here are my works on Yamabe Invariants:

Euclidean Domains with Nearly Maximal Yamabe Quotient, joint with Liam Mazurowski (01/2025).

On the Stability of the Yamabe invariant of $S^3$, joint with Liam Mazurowski (02/2024), to appear in Transactions of the AMS.

Improved Hebey-Vaugon conjecture on equivariant Yamabe invariants in dimension 3. joint with Tongrui Wang (09/2023)

The Yamabe Invariant of $RP^3$ via Harmonic Functions joint with Liam Mazurowski (05/2023)

On the Yamabe invariant of certain compact manifolds with boundary (02/2023), to appear in CVPDE

Here are my works on Mathematical Relativity:

Mass, Conformal Capacity, and the Volumetric Penrose Inequality. joint with Liam Mazurowski (10/2024), to appear in Comm. Anal. Geom.

Monotone Quantities for p-harmonic Functions and the Sharp p-Penrose inequality. joint with Liam Mazurowski (05/2023) ,to appear in Mathematical Research Letters.

Here are my works on minimal surfaces:

Minimal surfaces with low genus in lens spaces. joint with Xingzhe Li and Tongrui Wang (06/2024), Crelle's journal.

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