Related papers: A Slice Theorem for singular Riemannian foliations…

We prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section) which meets every…

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which…

In this paper we develop a theory of slice regular functions on a real alternative algebra $A$. Our approach is based on a well--known Fueter's construction. Two recent function theories can be included in our general theory: the one of…

We review the well-known slice theorem of Ebin for the action of the diffeomorphism group on the space of Riemannian metrics of a closed manifold. We present advances in the study of the spaces of Riemannian metrics, and produce a more…

In this note we analyze the C*-algebra associated with a branched covering both as a groupoid C*-algebra and as a Cuntz-Pimsner algebra. We determine conditions when the algebra is simple and purely infinite. We indicate how to compute the…

This work presents the basic elements and results of a Clifford algebra valued fractional slice monogenic functions theory defined from the null-solutions of a suitably fractional Cauchy-Riemann operator in the Riemann-Liouville and Caputo…

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally…

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…

This paper presents a simplified geometric proof of the Molino-Alexandrino-Radeschi (MAR) Theorem, which states that the closure of a singular Riemannian foliation on a complete Riemannian manifold is itself a smooth singular Riemannian…

We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…

We prove a version of Weyl's Law for the basic spectrum of a closed singular Riemannian foliation $(M,\mathcal{F})$ with basic mean curvature. In the special case of $M=\mathbb{S}^n$, this gives an explicit formula for the volume of the…

Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due…

In this paper, we lay the foundations of the theory of slice regular functions in several variables ranging in any real alternative $^*$-algebra, including quaternions, octonions and Clifford algebras. This theory is an extension of the…

We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a finitely generated fundamental group. Under additional topological or geometric assumptions…

Androulidakis and Skandalis showed how to associate a holonomy groupoid, a smooth convolution algebra and a C*-algebra to any singular foliation. In this note, we consider the singular foliations of a one-dimensional manifold given by…

In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize…

We prove that singular Riemannian foliations in Euclidean spheres can be defined by polynomial equations.

We present a new link between the Invariant Theory of infinitesimal singular Riemannian foliations and Jordan algebras. This, together with an inhomogeneous version of Weyl's First Fundamental Theorems, provides a characterization of the…

We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate…