# Diego CorroCardiff University | CU · School of Mathematics

Diego Corro

Doctor rerum naturalium

## About

20

Publications

1,194

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43

Citations

Introduction

My research interests are mainly in the fields of Riemannian geometry and differential topology. I am particularly interested in the relations between curvature bounds, geometry, and topology. My current research is focused on the study of manifolds admitting singular Riemannian foliations, and the geometric as well as the topological consequences that the presence of such foliations yields. I apply techniques from Riemannian submersions, algebraic topology and Alexandrov geometry.

Additional affiliations

March 2022 - August 2023

September 2021 - February 2022

September 2020 - August 2021

Education

September 2015 - July 2018

January 2013 - May 2015

August 2007 - June 2012

## Publications

Publications (20)

We show that, for each $n>1$, there exist infinitely many spin and non-spindiffeomorphism types of closed, smooth, simply-connected $(n+ 4)$-manifolds with a smooth,effective action of a torus $T^{n+2}$ and a metric of positive Ricci curvature invariant under a $T^{n}$-subgroup of $T^{n+2}$. As an application, we show that every closed, smooth, sim...

Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-changing solutions to Yamabe type problems, which are constant along the leaves of the foliation, and one positive solution of minimal energy among any other solution with...

We obtain an equivariant classification for orientable, closed, four-dimensional Alexandrov spaces admitting an isometric torus action. This generalizes the equivariant classification of Orlik and Raymond of closed four-dimensional manifolds with torus actions. Moreover, we show that such Alexandrov spaces are equivariantly homeomorphic to 4-dimens...

We present how to collapse a manifold equipped with a closed flat regular Riemannian foliation with leaves of positive dimension on a compact manifold, while keeping the sectional curvature uniformly bounded from above and below. From this deformation, we show that a closed flat regular Riemannian foliation with leaves of positive dimension on a co...

We prove that the group of isometries preserving a metric foliation on a closed Alexandrov space $X$, or a singular Riemannian foliation on a manifold $M$ is a closed subgroup of the isometry group of $X$ in the case of a metric foliation, or of the isometry group of $M$ for the case of a singular Riemannian foliation. We obtain a sharp upper bound...

We study RCD-spaces (X, d, m) with group actions by isometries preserving the reference measure m and whose orbit space has dimension one, i.e. cohomogeneity one actions. To this end we prove a Slice Theorem asserting that each slice at a point is homeomorphic to a non-negatively curved RCD-space. Under the assumption that X is non-collapsed we fur...

A singular foliation F on a complete Riemannian manifold M is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g. the partition of M into orbits of an isometric action. In this paper, we investigate variational problems in compact Riemannian manifolds equipped with SRF with special properties, e.g. isopa...

We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian (n+2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+2)$$\en...

Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-changing solutions to Yamabe type problems, which are constant along the leaves of the foliation, and one positive solution of minimal energy among any other solution with...

We expand upon the notion of a pre-section for a singular Riemannian foliation (M,F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M,\mathcal {F})$$\end{document}, i....

Let E be a smooth bundle with fiber an n-dimensional real projective space. We show that, if every fiber carries a positively curved pointwise strongly 1/4-pinched Riemannian metric that varies continuously with respect to its base point, then the structure group of the bundle reduces to the isometry group of the standard round metric on the projec...

We show that the integral foliated simplicial volume of a compact oriented smooth manifold with a regular foliation by circles vanishes.

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 concise proof for the existence of slices.

We show that for a smooth manifold equipped with a singular Riemannian foliation, if the foliated metric has positive sectional curvature, and there exists a pre-section, that is a proper submanifold retaining all the transverse geometric information of the foliation, then the leaf space has boundary. In particular, we see that polar foliations of...

Let $E$ be a smooth bundle with fiber an $n$-dimensional real projective space $\mathbb{R}P^n$. We show that, if every fiber carries a pointwise strongly $1/4$-pinched Riemannian metric that varies continuously with respect to its base point, then the structure group of the bundle reduces to the isometry group of the standard round metric on $\math...

We show that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a regular foliation by circles vanishes.

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 concise proof for the existence of slices.

We show that a singular Riemannian foliation of codimension $2$ on a compact simply-connected Riemannian $(n + 2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth effective $n$-torus action.

We obtain an equivariant classification for orientable, closed, four-dimensional Alexandrov spaces admitting an isometric torus action. This generalizes the equivariant classification of Orlik and Raymond of closed four-dimensional manifolds with torus actions. We also obtain a partial homeomorphism classification.