Wu, Jiayong
Published in
Chinese Annals of Mathematics, Series B

This paper deals with constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation ωt = Δω + aω ln ω on closed manifolds. A new interpolated Harnack inequality for ωt = Δω − ω ln ω+εRω on closed surfaces under ε-Ricci flow is also derived. Finally, the author proves a new differential Harnack inequality for ...

Huang, Zhangmin
Published in
Chinese Annals of Mathematics, Series B

Let π: Mn → Pn be an n-dimensional small cover over Pn and λ: ℱ(Pn) → ℤ2n be its characteristic function. The author uses the symbol c(λ) to denote the cardinal number of the image Im(λ). If c(λ) = n + 1 or n + 2, then a necessary and sufficient condition on the existence of spin structure on Mn is given. As a byproduct, under some special conditio...

Fang, Luobin
Published in
Chinese Annals of Mathematics, Series B

In this paper, the author extends Peter Li and Tian Gang’s results on the heat kernel from projective varieties to analytic varieties. The author gets an upper bound of the heat kernel on analytic varieties and proves several properties. Moreover, the results are extended to vector bundles. The author also gets an upper bound of the heat operators ...

Xie, Yi Lei, Peidong
Published in
Chinese Annals of Mathematics, Series B

In this paper the authors investigate the boundedness and almost periodicity of solutions of semilinear parabolic equations with boundary degeneracy. The equations may be weakly degenerate or strongly degenerate on the lateral boundary. The authors prove the existence, uniqueness and global exponential stability of bounded entire solutions, and als...

Xu, Hongwei Lei, Li Gu, Juanru
Published in
Chinese Annals of Mathematics, Series B

Let Mn(n ≥ 4) be an oriented compact submanifold with parallel mean curvature in an (n + p)-dimensional complete simply connected Riemannian manifold Nn+p. Then there exists a constant δ(n, p) 2 (0, 1) such that if the sectional curvature of N satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \u...

Zhang, Chuanjing
Published in
Chinese Annals of Mathematics, Series B

In this paper, the author proves a generalized Donaldson-Uhlenbeck-Yau theorem for twisted holomorphic chain on a non-compact Kähler manifold. As an application, the author obtains a Bogomolov type Chern numbers inequality for semistable twisted holomorphic chain.

Yang, Xu
Published in
Chinese Annals of Mathematics, Series B

In this paper, the author characterizes the subgroups of a finite metacyclic group K by building a one to one correspondence between certain 3-tuples (k,l,β) ∈ ℕ3 and all the subgroups of K. The results are applied to compute some subgroups of K as well as to study the structure and the number of p-subgroups of K, where p is a fixed prime number. I...

Nie, Liping Yang, Zongxin
Published in
Chinese Annals of Mathematics, Series B

In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ∥Sf∥ ≤ 6. Furthermore, any local...

Li, Huanhuan
Published in
Chinese Annals of Mathematics, Series B

For an upper triangular matrix ring, an explicit ladder of height 2 of triangle functors between homotopy categories is constructed. Under certain conditions, the author obtains a localization sequence of homotopy categories of acyclic complexes of injective modules.

Wang, Hongbin Liao, Fanghui
Published in
Chinese Annals of Mathematics, Series B

Let Ω ∈ Ls(Sn−1) (s > 1) be a homogeneous function of degree zero and b be a BMO function or Lipschitz function. In this paper, the authors obtain some boundedness of the Calderón-Zygmund singular integral operator TΩ and its commutator [b, TΩ] on Herz-Morrey spaces with variable exponent.