1 Contributo su Rivista

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Towering Phenomena for the Yamabe Equation on Symmetric Manifolds

Let (M, g) be a compact smooth connected Riemannian manifold (without boundary) of dimension N ≥ 7. Assume M is symmetric with respect to a point ξ_0 with non-vanishing Weyl’s tensor. We consider a linear perturbation of the Yamabe problem in (M, g). We prove that for any k ∈ ℕ, there exists ε_k > 0 such that for all ε ∈ (0, ε_k) the problem has a symmetric solution u_ε, which looks like the superposition of k positive bubbles centered at the point ξ_0 as ε → 0. In particular, ξ_0 is a t...

Bounded and unbounded capillary surfaces derived from the catenoid

We construct two kinds of capillary surfaces by using a perturbation method. Surfaces of first kind are embedded in a solid ball B of ℝ3 with assigned mean curvature function and whose boundary curves lie on the boundary of B: The contact angle along such curves is a non-constant function. Surfaces of second kind are unbounded and embedded in ℝ3 \ B'; B' being a deformation of a solid ball in ℝ3: These surfaces have assigned mean curvature function and one boundary curve on the boundary of B'...

Singly periodic free boundary minimal surfaces in a solid cylinder of H^2 x R

The aim of this work is to show there exist free boundary minimal surfaces of Saddle Tower type which are embedded in a vertical solid cylinder of H^2×R, H^2 being the hyperbolic plane, and invariant under the action of a vertical translation and a rotation. The number of boundary curves equals 2l,l⩾2. These surfaces come in families depending on one parameter and they converge to 2l vertical stripes having a common intersection line.

Improving Pumped Hydro Storage (PHS) Flexibility in China

Neurofilament Light Protein as a Biomarker in Severe Mental Disorders: A Systematic Review

Severe mental disorders (SMDs), such as schizophrenia (SZ), bipolar disorder (BD), and major depressive disorder (MDD), are heterogeneous psychiatric diseases that impose a significant societal burden due to their chronic disabling nature. There are no objective and reliable diagnostic tests for SMDs; thus, there is an urgent need for specific biomarkers to improve diagnosis, treatment, and resource allocation. Neurofilaments, found in cerebrospinal fluid and blood, offer reliable diagnostic ...

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