Related papers: Reeb flows without simple global surfaces of secti…

Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…

We prove that, for a $C^\infty$-generic contact form $\lambda$ adapted to a given contact distribution on a closed three-manifold, there exists a sequence of periodic Reeb orbits which is equidistributed with respect to $d\lambda$. This is…

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous.…

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is…

Let $(M, \xi)$ be a compact contact 3-manifold and assume that there exists a contact form $\alpha_0$ on $(M, \xi)$ whose Reeb flow is Anosov. We show this implies that every Reeb flow on $(M, \xi)$ has positive topological entropy. Our…

For each rational homology 3-sphere $Y$ which bounds simply connected definite 4-manifolds of both signs, we construct an infinite family of irreducible rational homology 3-spheres which are homology cobordant to $Y$ but cannot bound any…

In case of the heat flow on the free loop space of a closed Riemannian manifold non-triviality of Morse homology for semi-flows is established by constructing a natural isomorphism to singular homology of the loop space. The construction is…

We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the free homotopy classes of closed orbits of any pseudo-Anosov…

For a smooth function on a smooth manifold of a suitable class, the space of all connected components of preimages is the graph and called the {\it Reeb graph}. Reeb graphs are fundamental tools in the algebraic and differential topological…

For any link in the $3$-sphere, we give a visual construction of a stable map $f$ from the $3$-sphere into the real plane enjoying the following properties; $f$ has no cusp point, the set of definite fold points of $f$ is isotopic to the…

We study the flow of concentrated hard-sphere colloidal suspensions along smooth, non-stick walls using cone-plate rheometry and simultaneous confocal microscopy. In the glass regime, the global flow shows a transition from Herschel-Bulkley…

Among the topological conjugacy classes of the continuous flows $\{\phi^t\}$ whose orbit foliations are the planar Reeb foliation, there is one class called the standard Reeb flow. We show that $\{\phi^t\}$ is conjugate to the standard Reeb…

We give a detailed construction of a proper C^2-smooth function on R^4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C^2-smooth counterexample to the Hamiltonian…

Nondegenerate periodic orbits in three-dimensional Reeb flows can be classified into three types, positive hyperbolic, negative hyperbolic and elliptic. As a problem which involves refining the three-dimensional Weinstein conjecture, D.…

We study the existence of multiple closed Reeb orbits on some contact manifolds by means of $S^1$-equivariant symplectic homology and the index iteration formula. It is proved that a certain class of contact manifolds which admit…

We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a $3$-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan's homological…

We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux. We study two cases: when the monodromy map of the compatible open book is periodic and when it is…

In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to…

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some…

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…