A. Pigazzini

activity

20162026

collaborators

12 papers

math.DG2026

Yau's conjecture for the stacked Clifford tori of Wiygul

Alexander Pigazzini

We prove Yau's conjecture $λ_{1} = 2$ for the stacked Clifford tori of Wiygul: for all integers $N \geq 2$ , $k, ℓ \geq 1$ and every sufficiently large $m$ , every closed embedded minimal…

math.DG2026

A degenerate free boundary minimal annulus and non-uniqueness in spherical caps beyond the hemisphere

Alexander Pigazzini

Let ${Σ_{a}}$ , $a \in (0, 1/2)$ , be de Oliveira's family of embedded free boundary minimal annuli of revolution in geodesic balls $B (R (a)) \subset S^{3}$ , $R (a) > π /2$ . We prove th…

math.DG2026

Analytic local resolution of Medvedev's Morse index conjecture for the critical spherical catenoid in $H^{3}$

Alexander Pigazzini

Let $Σ_{a} \subset B^{3} (r (a)) \subset H^{3}$ ( $a > 1/2$ ) be the critical spherical catenoid of the Mori family, a free boundary minimal surface in the geodesic ball. The Medvedev co…

math.AP2026

Robin nullity and asymptotic geometry of the critical hyperbolic catenoid

Alexander Pigazzini

For each parameter $a > 1$ , the critical hyperbolic catenoid $Σ_{a}$ is a rotationally symmetric, free boundary minimal annulus in a geodesic ball $B^{3} (r (a)) \subset H^{3}$ . The M…

math.DG2026

The $r^{♯}$ invariant as a discriminant for the survival of the H-flux under T-duality on product manifolds

Alexander Pigazzini, Magdalena Toda

We show that the cohomological invariant $r^{♯}$ , introduced in [1] as a lower bound for the off-diagonal holonomy dimension of metric connections with totally skew torsion on p…

math.DG2026

Robin nullity in mode $∣ k ∣ = 1$ and asymptotic radius of the critical spherical catenoid

Alexander Pigazzini

Medvedev proved that the critical spherical catenoid $S i g m a_{a}$ , the rotationally symmetric free boundary minimal annulus in a geodesic ball $B^{3} (r (a))$ in $H^{3}$ from the family of…

math.DG2025

Local Topological Constraints on Berry Curvature in Spin--Orbit Coupled BECs

Alexander Pigazzini, Magdalena Toda

We establish a local topological obstruction to flattening Berry curvature in spin-orbit-coupled Bose-Einstein condensates (SOC BECs), valid even when the global Chern number vanis…

math.DG2025

Cohomologically Calibrated Affine Connections and Forced Irreducibility

Alexander Pigazzini, Magdalena Toda

We establish a principle of forced geometric irreducibility on product manifolds. We prove that for any product manifold $M = M_{1} \times M_{2}$ , a cohomologically calibrated affine conn…

math.DG2025

Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound

Alexander Pigazzini, Magdalena Toda

We establish a quantitative relationship between mixed de Rham classes and the geometric complexity of metric connections with totally skew torsion on product manifolds where both…

math.DG2025

Cohomologically calibrated affine connections and the Einstein condition on $S^{2} \times T^{2}$

Alexander Pigazzini, Magdalena Toda

This paper applies the recently developed framework of cohomologically calibrated affine connections to the fundamental problem of constructing non-Riemannian Einstein manifolds. I…

math.DG2025

Positive biorthogonal curvature on $S^{2} \times T^{2}$ via affine connection

Alexander Pigazzini

We address the long-standing problem of the existence of a Riemannian metric on $S^2\times T^2$ with strictly positive biorthogonal curvature ($ K_{\text{biort}}(σ) > 0 $). Thi…

math.DG2016

On totally umbilical isometric immersions with a special kind of Liouville metric in the R3 space

Alexander Pigazzini

The aim of this short article is to investigate the possibility of existence of totally umbilical isometric immersions in R^3 with isothermal parametrization and harmonic metric.

Yau's conjecture for the stacked Clifford tori of Wiygul

A degenerate free boundary minimal annulus and non-uniqueness in spherical caps beyond the hemisphere

Analytic local resolution of Medvedev's Morse index conjecture for the critical spherical catenoid in H3

Robin nullity and asymptotic geometry of the critical hyperbolic catenoid

The r♯ invariant as a discriminant for the survival of the H-flux under T-duality on product manifolds

Robin nullity in mode ∣k∣=1 and asymptotic radius of the critical spherical catenoid

Local Topological Constraints on Berry Curvature in Spin--Orbit Coupled BECs

Cohomologically Calibrated Affine Connections and Forced Irreducibility

Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound

Cohomologically calibrated affine connections and the Einstein condition on S2×T2

Positive biorthogonal curvature on S2×T2 via affine connection

On totally umbilical isometric immersions with a special kind of Liouville metric in the R3 space

Analytic local resolution of Medvedev's Morse index conjecture for the critical spherical catenoid in $H^{3}$

The $r^{♯}$ invariant as a discriminant for the survival of the H-flux under T-duality on product manifolds

Robin nullity in mode $∣ k ∣ = 1$ and asymptotic radius of the critical spherical catenoid

Cohomologically calibrated affine connections and the Einstein condition on $S^{2} \times T^{2}$

Positive biorthogonal curvature on $S^{2} \times T^{2}$ via affine connection