Xiaochun Rong's Home Page

• CV

  Teaching:

  • Introduction to the convergence and collapsing theory in Riemannian geometry, Fall, 2007
  • Syllabus

    Papers published:

    • The limiting eta-invariants on collapsed three-manifolds
    • The existence of polarized F-structure on volume collapsed 4-manifolds
    • Rationality of geometric signature of complete 4-manifolds
    • Collapsed manifolds with bounded diameter and bounded covering geometry
    • Existence of polarized F-structure on collapsed manifolds with bounded curvature and diameter
    • The almost cyclicity of the fundamental groups of positively curved manifolds
    • Positive curvature, local and global symmetry and fundamental groups
    • Collapsing vs. positive pincing
    • Positive pinching, volume and second Betti number
    • Fixed point free circle actions and finiteness theorems
    • Splittings and Cr-structures for manifolds with nonpositive sectional curvature
    • Curvature, diameter, homotopy groups, and homology rings
    • Positively curved manifolds with almost maximal symmetry rank
    • Collapsed Riemannian manifolds with bounded sectional curvature
    • The second twisted Betti number and the convergence of collapsing Riemannian manifolds
    • Positively curved manifolds with maximal discrete symmetry rank
    • Local splitting structures on nonpositively curved manifolds and semirigidity in dimension 3
    • On fundamental groups of positively curved manifolds with local torus actions
    • A connectedness principle in the geometry of positive curvature
    • The Hopf conjecture for manifolds with abelian group actions
    • Fundamental groups of closed manifolds with positive curvature and torus actions
    • Homeomorphism classification of positively curved manifolds with almost maximal symmetry rank
    • On fundamental groups of manifolds of positive sectional curvature
    • Collapsed manifolds with bounded sectional curvature and applications
    • Margulis lemma for compact Lie groups
    • Classification of fundamental groups of positively curved n-manifolds with symmetry rank >n/6

    Papers submitted:

    • Collapsed 5-manifolds with pinched positive sectional curvature
    • Collapsing construction with nilpotent structures
    • Fundamental groups of positively curved manifolds with symmetry

    Papers in progress: