Related papers: Poincar\'e problem for weighted projective foliati…
In this paper we give a complete local parametric classification of the hypersurfaces with dimension at least three of a space form that carry a totally geodesic foliation of codimension one. A classification under the assumption that the…
Poincar\'e profiles are a family of analytically defined coarse invariants, which can be used as obstructions to the existence of coarse embeddings between metric spaces. In this paper we calculate the Poincar\'e profiles of all connected…
This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…
We consider surjective endomorphisms f of degree > 1 on the projective n-space with n = 3, and f^{-1}-stable hypersurfaces V. We show that V is a hyperplane (i.e., deg(V) = 1) but with four possible exceptions; it is conjectured that deg(V)…
We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…
We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation…
We study weighted porous media equations on domains $\Omega\subseteq{\mathbb R}^N$, either with Dirichlet or with Neumann homogeneous boundary conditions when $\Omega\not={\mathbb R}^N$. Existence of weak solutions and uniqueness in a…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
We consider closed positive currents invariant by a singular holomorphic foliation on an algebraic surface. We show that under some conditions the foliation must leave invariant an algebraic curve.
We provide a Boseck-type basis of the space of holomorphic differentials for a large class of solvable covers of the projective line with perfect field of constants of characteristic $p > 0$. Within this class, we also describe the Galois…
In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…
This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on…
It was shown that in robustly transitive, partially hyperbolic diffeomorphisms on three dimensional closed manifolds, the strong stable or unstable foliation is minimal. In this article, we prove ``almost all'' leaves of both stable and…
This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound,…
This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. As far as stable solutions are concerned, we derive a new…
These are lecture notes of a course given in Pisa, SNS, in february 2002. They provide a classification of holomorphic foliations of nongeneral type on compact Kaehler surfaces.
We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$. Combining this with the result of Stibitz and Zhuang \cite{SZ19} on a relation between birational…
We give a lower bound for the delta invariant of the fundamental divisor of a quasi-smooth weighted hypersurface. As a consequence, we prove K-stability of a large class of quasi-smooth Fano hypersurfaces of index 1 and of all smooth Fano…
In this paper, we study nilpotent holomorphic foliations in complex dimension $n+1$, at the origin, defined by germs of integrable 1-forms whose linear part is given by \(zdz\). These foliations generalize the classical nilpotent foliations…
In this paper, we introduce the weighted mixed (sectional, Ricci and scalar) curvature of a foliated (and almost-product) Riemannian manifold $(M,g)$ equipped with a vector field $X$. We define several functions ($q$th Ricci type…