Related papers: Hard Lefschetz Property for Isometric Flows

We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Q^m for m > 2. We show that m is even, say m = 2k, and any such hypersurface is an open part of a tube around a k-dimensional complex projective space CP^k…

Let $(M,\omega)$ be a closed $2n$-dimensional semifree Hamiltonian $S^1$-manifold with only isolated fixed points. We prove that a density function of the Duistermaat-Heckman measure is log-concave. Moreover, we prove that $(M,\omega)$ and…

We find some curvature properties of 3-quasi-Sasakian manifolds which are similar to some well-known identities holding in the Sasakian case. As an application, we prove that any 3-quasi-Sasakian manifold of constant horizontal sectional…

We study the following rigidity problem in symplectic geometry:can one displace a Lagrangian submanifold from a hypersurface? We relate this to the Arnold Chord Conjecture, and introduce a refined question about the existence of relative…

In this paper we discuss the two-sided limit shadowing property for continuous flows defined in compact metric spaces. We analyze some of the results known for the case of homeomorphisms in the case of continuous flows and observe that some…

We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the $K$-theory and hyperbolic cohomology theory of flag varieties. We first show that, in $K$-theory, the two different choices of Kazhdan-Lusztig bases…

We prove some basic properties of Donaldson's flow of surfaces in a hyperkahler 4-manifold. When the initial submanifold is symplectic with respect to one K\"ahler form and Lagrangian with respect to another, we show that certain kinds of…

For projective varieties with a certain class of 'mild' isolated singularities and for projective threefolds with arbitrary Gorenstein canonical singularities, we show that the stringy Hodge numbers satisfy the Hard Lefschetz property. This…

In this note, we extend our previous work on the inverse $\sigma_k$ problem. Inverse $\sigma_{k}$ problem is a fully nonlinear geometric PDE on compact K\"ahler manifolds. Given a proper geometric condition, we prove that a large family of…

Let $(M,Q)$ be a compact, three dimensional manifold of strictly negative sectional curvature. Let $(\Sigma,P)$ be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let $\theta:\pi_1(\Sigma,P)\to\pi_1(M,Q)$ be a…

For the group PSL(2,Z) it is known that there is an isomorphism between polynomial eigenfunctions of the transfer operator for the geodesic flow and the Eichler cohomology in the theory of modular forms. In a recent paper by Chang and Mayer…

A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures…

In a well known work [Se], Graeme Segal proved that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding continuous mapping space through a range of dimensions…

If M is a riemannian manifold, then the inclusion of the complex of coclosed harmonic forms into the de Rham complex induces a linear isomorphism in cohomology. If M has at most countably many connected components, this linear isomorphism…

In this paper, we generalize the Heintze-Kobayashi-Wolf theory to homogeneous Finsler geometry, by proving two main theorems. First, any connected negatively curved homogeneous Finsler manifold is isometric to a Lie group endowed with a…

We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral…

We give a construction of the Floer homology of the pair of {\it non-compact} Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy which moves the infinity but leaves the intersection set of the…

We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…

An Independent Parallelism Theorem is proven in the theory of adhesive HLR categories. It shows the bijective correspondence between sequential independent and parallel independent direct derivations in the Weak Double-Pushout framework,…

We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that, when the genus of the surface is two, almost every such locally Hamiltonian flow with…