arXiv research

Study on spherical CR manifolds with non-trivial Chern classes.

Classifies involutions on spherical 3-manifolds.

Kähler-Ricci flow on spherical Fano manifolds converges to a soliton.

New theorem shows nearly spherical manifolds can be mapped from spheres.

Conformal qc geometry of spherical qc manifolds are investigated. We construct the qc Yamabe operators on qc manifolds, which are covariant under the conformal qc transformations. A qc manifold is scalar positive, negative or vanishing if and only if its qc Yamabe invariant is positive, negative or zero, respectively. …

The paper compares spectral geometry in hyperbolic and spherical manifolds.

Study spherical Fourier transform on hypergeometric type harmonic manifolds.

The paper finds hyperbolic small knots in many 3-manifolds.

Study inequalities involving torsional rigidity and spherical deficit on Riemannian manifolds.

Spherical Plateau problem studies minimal surfaces in quotients of spheres.

New 4-manifold invariant defined from trisection diagrams.

Paper connects two invariants of 3D manifolds using Hopf algebras.

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

The paper classifies Poincaré complexes as topological manifolds.

We give a complete classification of the spherical 3-manifolds that bound smooth rational homology 4-balls. Furthermore, we determine the order of spherical 3-manifolds in the rational homology cobordism group of rational homology 3-spheres. To this end, we use constraints for 3-manifolds to bound rational homology bal…

Study of line bundles on spherical varieties leads to Calabi-Yau metrics.

In this paper we classify the simply connected, spherical pseudohermitian manifolds whose Webster metric is CR-symmetric.

The paper classifies 3D spherical Sasakian manifolds using geometric and algebraic methods.

Motivated by the Turaev-Viro invariant of 3-manifolds, we construct a formal topological invariant of closed, oriented 3-manifolds involving spherical tetrahedra as an application of the asymptotic formula of 6j symbols for the Quantum Enveloping Algebra of sl(2). This invariant can be considered as a spherical version…

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

Suppose $M_{1}$ and $M_{2}$ are two closed (compact with no boundary) spherical CR manifolds with positive CR Yamabe constant. In this note, we show that the connected sum of $M_{1}$ and $M_{2}$ also admits a spherical CR structure with positive CR Yamabe constant.

We give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds. These lower and upper bounds are $C^{0}$-dependent on the metric coefficients. It gives better lower bounds for the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl.

Study $Θ$-invariants for spherical 3-manifolds via $\mathbb{Z}π$-homology equivalences.

The paper studies pseudo-isotopies of spherical 3-manifolds and computes ranks of certain groups.

Describes the space of spherical triangles on a smooth 3-manifold.

We construct closed symplectic manifolds for which spherical classes generate arbitrarily large subspaces in 2-homology, such that the first Chern class and cohomology class of the symplectic form both vanish on all spherical classes. We construct both Kaehler and non-Kaehler examples, and show independence of the cond…

New curvature positivity helps classify spherical spaces and complex projective spaces.

Study on Seifert fibered spherical 3-orbifolds, determining their unique fibrations.

We prove generalized lower Ricci bounds for Euclidean and spherical cones over compact Riemannian manifolds. These cones are regarded as complete metric measure spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricci curvature is bounded from below by n-1 satisfies the curvature-di…

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math …

Proves equality in Minkowski inequality for static, flat manifolds.

We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.

We obtain lower bounds for the first Laplacian eigenvalues of geodesic balls of spherically symmetric manifolds. These lower bounds are only $C^{0}$ dependent on the metric coefficients.

This paper connects geometric diagrams to spherical T-duality.

We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in $S^3$. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every…

Injectivity of geodesic ray transform on specific Finsler manifolds proven.

A new spherical Sliced-Wasserstein distance for data on spheres.

We prove generalized lower Ricci bounds for Euclidean and spherical cones over complete Riemannian manifolds. These cones are regarded as complete metric measure spaces. In general, they will be neither manifolds nor Alexandrov spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricc…

We determine the contributions of isolated singularities of spin V 4-manifolds to the index of the Dirac operator over them. From these data we derive certain constraints on the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds, and also on the embeddings of the real projective planes into 4-manif…

Rigidity theorem for spherical sectors in Riemannian manifolds.

Geometrically, spherical 3-manifolds emerge from flat SU(2)-bundles over hyperbolic surfaces.

We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology…

In this note, we first give a criterion of pseudo-Einstein contact forms and then affirm the CR analogue of Frankel conjecture in a closed, spherical, strictly pseudoconvex CR manifold of nonnegative pseudohermitian curvature on the space of smooth representatives of the first Kohn-Rossi cohomology group. Moreover, we …

Classifies 3-manifolds with uniformly positive scalar curvature.

Let M be a complete Riemannian manifold whose sectional curvature is bounded above by 1. We say that M has positive spherical rank if along every geodesic one hits a conjugate point at t=π. The following theorem is then proved: If M is a complete, simply connected Riemannian manifold with upper curvature bound 1 and po…

Stability conditions on K3 surfaces are linked to the masses of spherical objects.

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formulæ are presented.