26 citations · 98 across the 15 of their papers we have counts for
19 papers
A Vergleichsstellensatz of Strassen's Type for a Noncommutative Preordered Semialgebra through the Semialgebra of its Fractions
Tao Zheng, Lihong Zhi
Preordered semialgebras and semirings are two kinds of algebraic structures occurring in real algebraic geometry frequently and usually play important roles therein. They have many…
Positivity in Foliated Manifolds and Geometric Applications
Yashan Zhang, Tao Zheng
We introduce the notion of positivity for a real basic class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity…
Choosing the Variable Ordering for Cylindrical Algebraic Decomposition via Exploiting Chordal Structure
Haokun Li, Bican Xia, Huiying Zhang +1
Cylindrical algebraic decomposition (CAD) plays an important role in the field of real algebraic geometry and many other areas. As is well-known, the choice of variable ordering wh…
On almost quasi-negative holomorphic sectional curvature
Yashan Zhang, Tao Zheng
A recent celebrated theorem of Diverio-Trapani and Wu-Yau states that a compact Kähler manifold admitting a Kähler metric of quasi-negative holomorphic sectional curvature has an a…
Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups
Tao Zheng
The problem of computing \emph{the exponent lattice} which consists of all the multiplicative relations between the roots of a univariate polynomial has drawn much attention in the…
The Continuity Equation of the Gauduchon Metrics
Tao Zheng
We study the continuity equation of the Gauduchon metrics and establish its interval of maximal existence, which extends the continuity equation of the Kähler metrics introduced by…
Computing Multiplicative Relations between Roots of a Polynomial
Tao Zheng
Multiplicative relations between the roots of a polynomial in have drawn much attention in the field of arithmetic and algebra, while the problem of computing these…
The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
Ke Feng, Huabin Ge, Tao Zheng
We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori estimates which depend on the initial data on manif…
Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications
Ke Feng, Tao Zheng
We prove a priori estimates for a class of transverse fully nonlinear equations on Sasakian manifolds and give some geometric applications such as the transversion Calabi-Yau theor…
An Effective Framework for Constructing Exponent Lattice Basis of Nonzero Algebraic Numbers
Tao Zheng
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost…
An almost complex Chern-Ricci flow
Tao Zheng
We consider the evolution of an almost Hermitian metric by the part of its Chern-Ricci form on almost complex manifolds. This is an evolution equation first studied by Chu…
Higher dimensional generalizations of twistor spaces
Hai Lin, Tao Zheng
We construct a generalization of twistor spaces of hypercomplex manifolds and hyper-Kahler manifolds , by generalizing the twistor to a more general complex man…
A parabolic Monge-Ampère type equation of Gauduchon metrics
Tao Zheng
We prove the long time existence and uniqueness of solution to a parabolic Monge-Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the sol…
The Chern-Ricci flow on Oeljeklaus-Toma manifolds
Tao Zheng
We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus-Toma (OT-) manifolds which are non-Kähler compact complex manifolds with negati…
An upper bound of the heat kernel along the harmonic-Ricci flow
Shouwen Fang, Tao Zheng
In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration.…
Isoperimetric inequality along the twisted Kähler-Ricci flow
Shouwen Fang, Tao Zheng
We prove a uniform isoperimetric inequality for all time along the twisted Kähler-Ricci flow on Fano manifolds.
The (logarithmic) Sobolev inequalities along geometric flow and applications
Shouwen Fang, Tao Zheng
For some class of geometric flows, we obtain the (logarithmic) Sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non-collaps…
Inoue surfaces and the Chern-Ricci flow
Shouwen Fang, Valentino Tosatti, Ben Weinkove +1
We investigate the Chern-Ricci flow, an evolution equation of Hermitian metrics, on Inoue surfaces. These are non-Kahler compact complex surfaces of type Class VII. We show that, a…
Estimates of the gaps between consecutive eigenvalues of Laplacian
Daguang Chen, Tao Zheng, Hongcang Yang
By the calculation of the gap of the consecutive eigenvalues of with standard metric, using the Weyl's asymptotic formula, we know the order of the upper bound of this g…