Biao Ma

activity

20192026

most citedConstant Q-curvature metrics on conic 4-manifolds

3 citations · 4 across the 18 of their papers we have counts for

collaborators

21 papers

math.AP2026

Spectral Gårding Elliptic Equations

Hao Fang, Biao Ma

We study spectral Gårding elliptic equations on compact Kähler manifolds. Smooth solvability is equivalent to the existence of a smooth representative in the admissible domain. The…

math.DG2026

The $J$ -Null Locus and Local Regularity of Weak Solutions of the Semistable $J$ -Equation

Hao Fang, Biao Ma

For the semistable $J$ -equation, we prove that the numerical $J$ -null locus coincides with the ambient $C^{2}$ -singular locus of Murakami's weak solution. Consequently, this singular…

math.AP2026

Determinantal capacity and $L^{\infty}$ -Estimates

Hao Fang, Biao Ma, Jinyang Wu

We introduce determinantal ellipticity, or det-ellipticity, a quantitative structural condition for fully nonlinear elliptic operators on compact Kähler manifolds that provides the…

math.AP2026

Liouville Rigidity for Real and Complex Degenerate Hessian Equations

Hao Fang, Biao Ma, Jinyang Wu

We prove Liouville rigidity theorems for translation-invariant real and complex Hessian equations in the viscosity sense, where the PDE is encoded by an admissible set $\mathcal{A}…

math.CO2026

Ideal Gårding polynomials

Hao Fang, Biao Ma

We introduce ideal Gårding polynomials, a convexity-enhanced subclass of Gårding polynomials whose Gårding components are recursively convex under partial differentiation. This cla…

math.GT2026

Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups

Tamunonye Cheetham-West, Tam Cheetham-West, Biao Ma +2

We prove that, whenever the monodromy maps are fully-punctured, the finite quotients of a fibered hyperbolic $3$ -manifold group detect the taut polynomials of the fibered faces of…

math.CO2026

Gårding Polynomials

Hao Fang, Biao Ma

We introduce Gårding polynomials, a class of real multivariate polynomials characterized by positivity regions that are invariant under translation by positive vectors and closed u…

math.DS2026

Construction of Anosov flows on fibered hyperbolic 3-manifolds

François Béguin, Christian Bonatti, Biao Ma +1

We prove that fibered hyperbolic $3$ -manifolds carrying transitive Anosov flows are abundant. More precisely, for every $g \geq 2$ , there is a finite index subgroup~ $Γ$ of $ \mathrm…

math.MG2025

Cocycle superrigidity for median spaces of finite rank

Biao Ma, Lamine Messaci

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrig…

math.DG2025

Existence of complete conformal metrics on $R^{n}$ with prescribed Q-curvature

Mingxiang Li, Biao Ma

Given a smooth function $f (x)$ on $R^{n}$ which is positive somewhere and satisfies $f (x) = O (∣ x ∣^{- l})$ for any $l > \frac{n}{2}$ , we show that there exists a complete and conf…

math.DG2025

Constructing stable Hilbert bundles via Diophantine approximation

Yucheng Liu, Biao Ma

On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian--Einstein metrics. Our main constructive step is by investigating the…

math.GT2023

Dynamics of subgroups of mapping class groups

Ilya Gekhtman, Biao Ma

Let $Mod (S)$ be the mapping class group of a closed orientable surface $S$ of genus $g \geq 2$ . Let $G$ be a non-elementary subgroup of $Mod (S)$ so that the associated Bo…

math.AP2023

On a fully nonlinear elliptic equation with differential forms

Hao Fang, Biao Ma

We introduce a fully nonlinear PDE with a differential form $Λ$ , which unifies several important equations in Kähler geometry including Monge-Ampère equations, J-equations, inverse…

math.GT2022

Boundary representations of mapping class groups

Biao Ma

Let $S = S_{g}$ be a closed orientable surface of genus $g \geq 2$ and $M o d (S)$ be the mapping class group of $S$ . In this paper, we show that the boundary representation of $M o d (S)$ …

math.AP2022

A Liouville's theorem for some Monge-Ampère type equations

Hao Fang, Biao Ma, Wei Wei

We study a Monge-Ampère type equation that interpolates the classical {σ_2} -Yamabe equation in conformal geometry and the 2-Hessian equation in dimension 4.

math.DG2020

Curve shortening flow on Riemann surfaces with possible ambient conic singularities

Biao Ma

In this paper, we study the curve shortening flow (CSF) on Riemann surfaces. We generalize Huisken's comparison function to Riemann surfaces and surfaces with conic singularities.…

math.DG2020

A Note On Andrews Inequality

Hao Fang, Biao Ma, Wei Wei

We prove some extensions of Andrews inequality.

math.DG2019★ 3 cited

Constant Q-curvature metrics on conic 4-manifolds

Hao Fang, Biao Ma

We consider the constant Q-curvature metric problem in the given conformal class on conic 4-manifolds and study related differential equations.

math.GT2019

On a family of unitary representations of mapping class groups

Biao Ma

For a compact surface $S = S_{g, n}$ with $3 g + n \geq 4$ , we introduce a family of unitary representations of the mapping class group Mod( $S$ ) based on the space of measured foliat…

math.RT2019

Combinatorics of faithfully balanced modules

William Crawley-Boevey, Biao Ma, Baptiste Rognerud +1

We study and classify faithfully balanced modules for the algebra of lower triangular $n$ by $n$ matrices. The theory extends known results about tilting modules, which are classif…

math.RA2019★ 1 cited

On faithfully balanced modules, F-cotilting and F-Auslander algebras

Biao Ma, Julia Sauter

We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category ${\rm cogen…

Spectral Gårding Elliptic Equations

The J-Null Locus and Local Regularity of Weak Solutions of the Semistable J-Equation

Determinantal capacity and L∞-Estimates

Liouville Rigidity for Real and Complex Degenerate Hessian Equations

Ideal Gårding polynomials

Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups

Gårding Polynomials

Construction of Anosov flows on fibered hyperbolic 3-manifolds

Cocycle superrigidity for median spaces of finite rank

Existence of complete conformal metrics on Rn with prescribed Q-curvature

Constructing stable Hilbert bundles via Diophantine approximation

Dynamics of subgroups of mapping class groups

On a fully nonlinear elliptic equation with differential forms

Boundary representations of mapping class groups

A Liouville's theorem for some Monge-Ampère type equations

Curve shortening flow on Riemann surfaces with possible ambient conic singularities

A Note On Andrews Inequality

Constant Q-curvature metrics on conic 4-manifolds

On a family of unitary representations of mapping class groups

Combinatorics of faithfully balanced modules

On faithfully balanced modules, F-cotilting and F-Auslander algebras

The $J$ -Null Locus and Local Regularity of Weak Solutions of the Semistable $J$ -Equation

Determinantal capacity and $L^{\infty}$ -Estimates

Existence of complete conformal metrics on $R^{n}$ with prescribed Q-curvature