The existence of closed 3-forms of $\tilde G_2$-type on 7-manifolds

The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension

The existence of light-like homogeneous geodesics in homogeneous Lorentzian manifolds

The Existence of Soliton Metrics for Nilpotent Lie Groups

The Existence of Type II Singularities for the Ricci Flow on $S^{n+1}$

The existence problem for Steiner networks in strictly convex domains

The existence results for solutions of indefinite scalar curvature problem

The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature

The explicit formula of flat Lagrangian H-umbilical submanifolds in quaternion Euclidean spaces

The extension and convergence of mean curvature flow in higher codimension

The Extension for Mean Curvature Flow with Finite Integral Curvature in Riemannian Manifolds

The extrinsic curvature of entire minimal graphs in $\H^2\times\R$

The extrinsic holonomy Lie algebra of a parallel submanifold

The Faddeev-Mickelsson-Shatashvili anomaly and lifting bundle gerbes

The Family Blowup Formula of the Family Seiberg-Witten Invariants

The Feller property on Riemannian manifolds

The Fermi Flow and its Application to Geometry

The first $L^2$-Betti number for classifying spaces of variations of Hodge structures

The first bifurcation point for Delaunay nodoids

The first cohomology of the mapping class group with coefficients in algebraic functions on the SL(2, C) moduli space