We show that an embedded minimal annulus Σ ⊂ B which intersects ∂B orthogonally and is invariant under reflection through the coordinate planes is the critical catenoid. The proof uses nodal domain arguments and a characterization, due to Fraser and Schoen, of the critical catenoid as the unique free boundary minimal annulus in Bn with lowest Steklov eigenvalue equal to 1. We also give more gen...

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard–Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary–symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from the superbosonization formul...

Conjecture. Let G be a compact Lie group which acts isometrically on a complete Riemannian manifold M , such that this action admits a section: There exists a closed submanifold Σ in M which meets each orbit orthogonally. Then the space Ωhor(M) of all differential forms on M which are invariant under the G-action and are horizontal in the sense that they kill each vector which is tangent to an ...

Orthogonal approximate message-passing (OAMP) is proposed for signal recovery from right-orthogonally invariant linear measurements with spatial coupling. Conventional state evolution generalized to a unified framework of the coupling and long-memory case. The used formulate so-called Onsager correction in OAMP spatially coupled systems. recursion Bayes-optimal proved converge systems via its e...

In this paper, we study a class of Finsler metrics with orthogonal invariance. We find an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence, we show that all orthogonally invariant Finsler metrics of almost vanishing H-curvature are of almost vanishing Ξ-curvature and corresponding one forms are exact, generalizing a result previously only known...