Related papers: Minimizability of developable Riemannian foliation…

In this paper we prove that given a pair $(X,D)$ of a threefold $X$ and a boundary divisor $D$ with mild singularities, if $(K_X+D)$ is movable, then the orbifold second Chern class $c_2$ of $(X,D)$ is pseudo-effective. This generalizes the…

We obtain a characterisation of confined subgroups of Thompson's group $F$. As a result, we deduce that orbital graph of a point under action of $F$ has uniformly subexponential growth if and only if this point is fixed by the commutator…

For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.

We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…

Let $f:\mathbb{Q}\to \mathbb{Q}$ be a function definable in an o-minimal expansion of $(\mathbb{Q},<,+,0)$. We show that $f$ is eventually linear. In addition, we show that this holds in every elementary equivalent structure.

In this paper, we prove that any surface corresponding to linear second-order ODEs as a submanifold is minimal in all classes of third-order ODEs $y'''=f(x, y, p, q)$ as a Riemannian manifold where $y'=p$ and $y''=q$, if and only if…

A matchbox manifold is a foliated space with totally disconnected transversals, and an equicontinuous matchbox manifold is the generalization of Riemannian foliations for smooth manifolds in this context. In this paper, we develop the…

This article proves that if M is a smooth manifold of dimension at least four, then for generic choice of metric on M, all prime parametrized minimal surfaces in M are free of branch points and lie on nondegenerate critical submanifolds for…

The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifold (M^m,h) with m>2. The goal of the paper is twofold, on…

We investigate singular Finsler foliations (SFFs) on a manifold equipped with an $(\alpha,\beta)$-metric. To be precise, we verify that any SFF of an $(\alpha,\beta)$-space is, under some hypotheses on the metric, a singular Riemannian…

Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces $-$ minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones.…

The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm…

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially…

In this paper, we construct in characteristic zero a derived foliation on derived mapping stacks $\underline{\mathbf{Map}}_S(X,Y)$, for $S$ a base derived stack, $X$ a proper schematic, flat, and local complete intersection derived stack…

We prove a generalisation of Bott's vanishing theorem for the full transverse frame holonomy groupoid of any transversely orientable foliated manifold. As a consequence we obtain a characteristic map encoding both primary and secondary…

In this paper, the Almeida-Molino obstruction to developability of transversely complete foliations is extended to Lie groupoids.

Let $(M, g)$ be an asymptotically flat Riemannian $3$-manifold with non-negative scalar curvature and positive mass. We show that each leaf of the canonical foliation through stable constant mean curvature surfaces of the end of $(M, g)$ is…

In this paper, we study the holomorphic foliations admitting a common invariant algebraic set $C$ defined by a polynomial $f$ in $ \mathbb{K}[x_1,x_2,...,x_n]$ over any characteristic $0$ subfield $\mathbb{K}\subseteq\mathbb{C}$. For the…

We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, provided that the singular foliation defined by the closures of…

We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation} \mathcal{F}(u,\Omega):=\int_\Omega \left[ f(x,Du)- g \cdot u \right] dx , \notag \end{equation}…