On the mod p Betti numbers of loop spaces.
On the moduli space of superminimal surfaces in spheres.
On the motion of a curve by its binormal curvature
We propose a weak formulation for the binormal curvature flow of curves in . This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to hold, as long as self-intersections do not occur. We also prove a global existence theorem in that framework.
On the multiplicity of eigenvalues of conformally covariant operators
Let be a compact Riemannian manifold and an elliptic, formally self-adjoint, conformally covariant operator of order acting on smooth sections of a bundle over . We prove that if has no rigid eigenspaces (see Definition 2.2), the set of functions for which has only simple non-zero eigenvalues is a residual set in . As a consequence we prove that if has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics in the -topology....
On the natural operators of Bianchi type
On the Nature of Thin Complements of Complete Kähler Metrics.
On the Nonexistence of a Hypersurface of Prescribed Mean Curvature with a Given Boundary.
On the non-existence of certain ovaloids
On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture
Let M̅ be a compact Riemannian manifold with sectional curvature satisfying (resp. ), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.
On the normality of an almost contact -structure on -submanifolds
We study -dimensional -submanifolds of -dimension immersed in a quaternionic space form , , and, in particular, determine such submanifolds with the induced normal almost contact -structure.
On the nullity index of isometric immersions of Kähler manifolds
On the Number of Closed Geodesics on Projective Spaces.
On the number of minimal two-spheres of small area in manifolds with curvature bounded above.
On the operator of exterior derivation on the Riemannian manifolds with cylindrical ends.
On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the persistence of pseudo-holomorphic curves on an almost complex torus (with an appendix by Jügen Pöschel).
On the Petersson-Weil metric for the moduli space of Hermite-Einstein bundles and its curvature.
On the Pick invariant
On the Polynomial Cohomology of Affine Manifolds.