5 papers
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.
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…