O(p + 1) x O(p + 1)-Invariant hypersurfaces with zero scalar curvature in euclidean space

Op-brai140199 1..1

Sir, I read with great interest the article by Maller et al. (2014) concerning occipital bending and its association with depression. While there is a large body of sound and most interesting literature on brain asymmetry, I think that in some of these studies the brain is regarded in total isolation thereby neglecting its surrounding structures with their complicated anatomic inter-relationshi...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hypersurfaces with Constant Scalar Curvature in a Hyperbolic Space Form

Let M be a complete hypersurface with constant normalized scalar curvature R in a hyperbolic space form H. We prove that if R̄ = R + 1 ≥ 0 and the norm square |h| of the second fundamental form of M satisfies nR̄ ≤ sup |h| ≤ n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], then either sup |h| = nR̄ and M is a totally umbilical hypersurface; or sup |h| = n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], and M i...

Hypersurfaces with Constant Scalar Curvature

Let M be a complete two-dimensional surface immersed into the three-dimensional Euclidean space. Then a classical theorem of Hilbert says that when the curvature of M is a non-zero constant, M must be the sphere. On the other hand, when the curvature of M is zero, a theorem of Har tman-Nirenberg [4] says that M must be a plane or a cylinder. These two theorems complete the classification of com...

Op-brai150410 1..15

Alzheimer’s disease is a multifactorial dementia disorder characterized by early amyloid-b, tau deposition, glial activation and neurodegeneration, where the interrelationships between the different pathophysiological events are not yet well characterized. In this study, longitudinal multitracer positron emission tomography imaging of individuals with autosomal dominant or sporadic Alzheimer’s ...