相关论文: Foliations with complex leaves and instability for…
We give a complex polarized variation of Hodge structure over a compact K"ahler manifold $M$ which controls all finite-dimensional complex polarized variations of Hodge structure over $M$ and their tensor relations. As a corollary, we…
In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a…
Let M be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the M-isoperiodic foliation are either all closed or all dense. In the second case, we establish ergodicity of the…
We study a Floer-theoretic approach to harmonic maps from the two-torus into non-flat K\"ahler manifolds. Building on the complex-regularized polysymplectic (CRPS) formalism of [BF24], which provides a Hamiltonian description of harmonic…
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type…
We call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian…
We study instabilities of the system composed of stationary scalar fields and asymptotically flat horizonless reflecting compact stars. In the probe limit, we obtain bounds on the scalar field frequency. Below this bound, stationary hairy…
The leafwise cohomology of the weak stable foliation of the geodesic flows is very important in the study of the space of actions whose orbit foliation is the weak stable foliation of geodesic flows.The dimension one cohomology was computed…
We give necessary and sufficient conditions for a Lagrangian submanifold of a K\"ahler manifold to be biharmonic. Furthermore, we classify biharmonic PNMC Lagrangian submanifolds in the complex space forms.
All compact K\"ahler, or even $\partial\bar\partial$-manifolds, are rationally formal. Not all of them are strongly formal. Yet some of them are: For complete smooth complex toric varieties and homogeneous compact K\"ahler manifolds we show…
We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimising properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable…
Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, specially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations…
Let (M,F) be a foliated manifold. We study the relationship between the basic cohomology Hb(M,F) of the foliation and the De Rham cohomology H(DF) of the space of leaves M/F as a quotient diffeological space. We prove that for an arbitrary…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth…
Given a smooth foliation by complex curves (locally around a point $x\in\mathbb{C}^2\setminus\{0\}$) which is "compatible" with the foliation by spheres centered at the origin, we construct a smooth real-valued function $g$ in a…
We use perturbations in order to study the stability of the Cauchy Horizon in a Reissner-Nordstr\"om space-time. The perturbations are either scalar or gravitational, and indicate some strong instabilities.
In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves…
A foliation F on a Riemannian manifold M is homogeneous if its leaves coincide with the orbits of an isometric action on M. A foliation F is polar if it admits a section, that is, a connected closed totally geodesic submanifold of M which…
We present reformulation of Mathieu's result on representing cohomology classes of symplectic manifold with symplectically harmonic forms. We apply it to the case of foliated manifolds with transversally symplectic structure and to…