2 citations · 2 across the 10 of their papers we have counts for
11 papers
A relative Toponogov comparison theorem
Jianming Wan
We present a relative form of the Toponogov comparison theorem.
Harmonic 2-forms and positively curved 4-manifolds
Kefeng Liu, Jianming Wan
We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a Kato type inequality, then it is definite. We also discuss some new insights for comp…
Integral of distance function on compact Riemannian manifolds
Jianming Wan
In this paper we show that, under some curvature assumptions the integral of distance function on a compact Riemannian manifold is bounded below by the product of diameter, volume…
Harmonic maps from to Kahler manifolds
Jianming Wan
In this paper, we shall prove that a harmonic map from () to any Kahler manifold must be holomorphic under an assumption of energy density. It can be consi…
On the fundamental group of complete manifolds with almost Euclidean volume growth
Jianming Wan
It is proved that the fundamental group of a complete Riemannian manifold with nonnegative Ricci curvature and certain volume growth conditions is trivial or finite.
An extension of Bonnet-Myers theorem
Jianming Wan
We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.
Manifolds tightly covered by two metric balls
Jianming Wan
In this note we provide natural optimal geometric conditions for a Riemannian manifold suitably covered by two open metric balls to be homeomorphic to a sphere. This can be viewed…
Curvature and integrability of almost complex structures
Jianming Wan
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an at…
A result on Ricci curvature and the second Betti number
Jianming Wan
We prove that the second Betti number of a compact Riemannian manifold vanishes under certain Ricci curved restriction.
Degrees of periods
Jianming Wan
We introduce the concept of degree to classify the periods in the sense of Kontsevich. Using this notion we give some new understanding of some problems in transcendental number th…
Harmonic Complex Structures
Jianming Wan
In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermedi…