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We prove a conjecture of Knutson asserting that the Schubert structure constants of the cohomology ring of a two-step flag variety are equal to the number of puzzles with specified borde...
We prove the Conley conjecture for negative monotone, closed symplectic manifolds, i.e., the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of such manifolds.
We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian mani...
We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly posi...
Smooth metric measure spaces have been studied from the two different perspectives of Bakry-\'Emery and Chang-Gursky-Yang, both of which are closely related to work of Perelman on the Ricci flow. The...
We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We a...
We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.
We prove an analogue for odd dimensional manifolds with boundary, in the $b$-calculus setting, of the higher Atiyah-Patodi-Singer index theorem by Getzler and by Wu.
In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guarant...
We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Rie...
We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. The...
To a rational homology sphere graph manifold one can associate a weighted tree invariant called splice diagram. It was shown earlier that the splice diagram determines the universal abelian cover of ...
For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geode...
We prove finiteness of the number of smooth blow-downs on Fano manifolds and boundedness results for the geometry of non projective Fano-like manifolds. Our proofs use properness of Hilbert schemes an...
We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle...

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