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Masoumeh Zarei

Publications and source records attributed to Masoumeh Zarei.

12 recordsLinked to original sources
arXiv2026

Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds

We prove a vanishing theorem for the local Betti numbers of closed, $n$-dimensional Riemannian manifolds with a lower volume bound, an upper diameter bound, and a lower intermediate Ricci curvature bound. This generalizes and interpolates between known results under lower sectional and Ricci curvature bounds. Moreover, the methods extend to open manifolds, yielding a corresponding vanishing theorem for the global Betti numbers.

math.DG↗
arXiv2026

Precompactness for homogeneous Einstein metrics on torus bundles

We prove a precompactness result for homogeneous Einstein metrics on the set of homogeneous torus bundles over a common base. This set can contain infinite families of compact simply connected homogeneous torus bundles over a common simply connected base with toral fibres of fixed dimension.

math.DG↗
arXiv2026

Ricci Flow Preserves Positive Sectional Curvature on Homogeneous Spheres

We prove that the Ricci flow preserves positive sectional curvature on homogeneous spheres and complex projective spaces. In conjunction with prior results, this completes the classification of which homogeneous spaces have positively curved metrics flowing outside the set of positively curved metrics and which do not.

math.DG↗
arXiv2025

Positive intermediate curvatures and Ricci flow

We show that, for any $n\geq 2$, there exists a homogeneous space of dimension $d=8n-4$ with metrics of $\mathrm{Ric}_{\frac{d}{2}-5}>0$ if $n\neq 3$ and $\mathrm{Ric}_6>0$ if $n=3$ which evolve under the Ricci flow to metrics whose Ricci tensor is not $(d-4)$-positive. Consequently, Ricci flow does not preserve a range of curvature conditions that interpolate between positive sectional and positive scalar curvature. This extends a theorem of Böhm and Wilking in the case of $n=2$.

math.DG↗
arXiv2025

Ricci flow from singular spaces with bounded curvature

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow converges in the $C^{1,α}$-sense to a $C^{1,α}$-continuous Riemannian manifold which is isometric to the original metric space. Moreover, we prove that the flow is uniquely determined by the initial condition, up to isometry.

math.DG↗
arXiv2024

On the Geometry and Topology of Positively Curved Eschenburg Orbifolds

The present article explores the relationship between positive sectional curvature and the geometric and topological properties of Eschenburg $6$-orbifolds. First, we prove that positive sectional curvature imposes restrictions on the their singular sets, thereby confirming a conjecture posed by Florit and Ziller. Then we compute the orbifold cohomology rings for those with a specific singular locus. This reveals a distinctive behavior in the cohomology groups of positively curved Eschenburg orbifolds compared to their non-negatively curved counterparts. Furthermore, we compute the orbifold cohomology rings of all Eschenburg orbifolds.

math.DG↗
arXiv2022

The flavour of intermediate Ricci and homotopy when studying submanifolds of symmetric spaces

We introduce a new technique to the study and identification of submanifolds of simply-connected symmetric spaces of compact type based upon an approach computing $k$-positive Ricci curvature of the ambient manifolds and using this information in order to determine how highly connected the embeddings are. This provides codimension ranges in which the Cartan type of submanifolds satisfying certain conditions which generalize being totally geodesic necessarily equals the one of the ambient manifold. Using results by Guijarro--Wilhelm our approach partly generalizes recent work by Berndt--Olmos on the index conjecture.

math.DG↗
arXiv2022

Torus actions on Alexandrov 4-spaces

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 $4$-dimensional Riemannian orbifolds with isometric $T^2$-actions. We also obtain a partial homeomorphism classification.

math.DG↗
arXiv2019

On the equivariant cohomology of cohomogeneity one Alexandrov spaces

We give a characterization of those Alexandrov spaces admitting a cohomogeneity one action of a compact connected Lie group $G$ for which the action is Cohen--Macaulay. This generalizes a similar result for manifolds to the singular setting of Alexandrov spaces where, in contrast to the manifold case, we find several actions which are not Cohen--Macaulay. In fact, we present results in a slightly more general context. We extend the methods in this field by a conceptual approach on equivariant cohomology via rational homotopy theory using an explicit rational model for a double mapping cylinder.

math.DG↗
arXiv2017

Cohomogeneity one Alexandrov spaces in low dimensions

We classify closed, simply-connected cohomogeneity-one Alexandrov spaces in dimensions $5$, $6$ and $7$. We show that every closed, simply-connected smooth $n$-orbifold, $2\leq n\leq 7$ with a cohomogeneity one action is equivariantly homeomorphic to a smooth good orbifold of cohomogeneity one.

math.DG↗
arXiv2015

Cohomogeneity one topological manifolds revisited

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological manifolds in dimensions $5$, $6$, and $7$ and obtain topological characterizations of these spaces. In these dimensions, these manifolds are homeomorphic to smooth manifolds.

math.GT↗