Related papers: A conformal integral invariant on Riemannian folia…

On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe…

We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…

Let $\FF$ be a codimension one foliation on a closed manifold $M$ which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.

We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally…

Given a compact four dimensional smooth Riemannian manifold $(M,g)$ with smooth boundary, we consider the evolution equation by $Q$-curvature in the interior keeping the $T$-curvature and the mean curvature to be zero and the evolution…

We extend Fourier analysis to curved spaces by defining a Generalized Fourier Transform (GFT) on any Riemannian manifold $\Sigma$ via spectral decomposition. Under minimal requirements that the transform is an isometric isomorphism and has…

We consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ with a Riemannian metric $g$ of negative curvature with fixed total area. The second author has shown that the topological entropy of geodesic flow for $g$ is greater than…

On a Riemannian 2-torus $(T^2,g)$ we study the geodesic flow in the case of low complexity described by zero topological entropy. We show that this assumption implies a nearly integrable behavior. In our previous paper \cite{GK} we already…

We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical…

Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n \geq 25$ with positive Yamabe invariant $Y(M,g_0)>0$ and positive fourth-order invariant $Y_4(M,g_0)>0$. We show that, arbitrarily $C^1$-close to $g_0$, there exists a Riemannian…

In this paper, we provide the lower bounds of the first non-zero basic eigenvalue on a closed singular Riemannian manifold $(M,\mathcal{F})$ with basic mean curvature that depends on the given non-negative lower bound of the Ricci curvature…

A conformal metric $g$ with constant curvature one and finite conical singularities on a compact Riemann surface $\Sigma$ can be thought of as the pullback of the standard metric on the 2-sphere by a multi-valued locally univalent…

We investigate the combinatorial analogues, in the context of normal surfaces, of taut and transversely measured (codimension 1) foliations of 3-manifolds. We establish that the existence of certain combinatorial structures, a priori weaker…

We prove that given any compact Riemannian 3-manifold with boundary M, there exists a smooth properly embedded one-manifold G, included in M, each of whose components is a simple closed curve and such that the domain D=Int(M)-G does not…

In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the GJMS operators, which include the Yamabe and Paneitz operators. We give several…

The main result of this paper is the following: any `weighted' Riemannian manifold $(M,g,\mu)$ - i.e. endowed with a generic non-negative Radon measure $\mu$ - is `infinitesimally Hilbertian', which means that its associated Sobolev space…

The basic cohomology of a Riemannian foliation on a complete manifold with all leaves closed is the cohomology of the leaf space. In this paper we introduce various methods to compute the basic cohomology in the presence of both closed and…

We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and…

Let $(M,g)$ be a pseudo-Riemannian manifold and $F_\lambda(M)$ the space of densities of degree $\lambda$ on $M$. We study the space $D^2_{\lambda,\mu}(M)$ of second-order differential operators from $F_\lambda(M)$ to $F_\mu(M)$. If $(M,g)$…

For a Riemannian manifold with dimension at least six, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.