This note studies Arveson’s curvature invariant for d-contractions T = (T1, T2, . . . , Td) for the special case d = 1, referring to a single contraction operator T on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a single contraction. The formula is applied to give an example of an operator with nonintegral curvature. Under the additio...

Abstract. We give sufficient conditions for a measured length space (X, d, ν) to admit local and global Poincaré inequalities. We first introduce a condition DM on (X, d, ν), defined in terms of transport of measures. We show that DM , together with a doubling condition on ν, implies a scale-invariant local Poincaré inequality. We show that if (X, d, ν) has nonnegative N -Ricci curvature and ha...

H. Kurebayashi, 2, ∗ Jairo Sinova, 4, 5 D. Fang, A. C. Irvine, T. D. Skinner, J. Wunderlich, 6 V. Novák, R. P. Campion, B. L. Gallagher, E. K. Vehstedt, 5 L. P. Zârbo, K. Výborný, A. J. Ferguson, † and T. Jungwirth 7 Microelectronics Group, Cavendish Laboratory, University of Cambridge, CB3 0HE, UK PRESTO, Japan Science and Technology Agency, Kawaguchi 332-0012, Japan Institut für Physik, Johan...

Macroscopic, description.?The specimen consisted of an irregular reddish-yellow firm tumour and a living round worm. The tumour measured '?0 X 6.5 X 3.0 cm. and was situated in the great omentum below the greater curvature oi Mie stomach. It was apparently covered with smooth dull-looking peritoneum and at one place was overlaid by a few dark-red blood ('lots. On serial section it was found to ...

While there is a rich literature on methods for computing the curvature of discrete surfaces, the case of discrete surfaces with boundary is often ignored. We show how to compute curvature measures for discrete surfaces with boundary using the theory of normal cycles. Our curvature formulae for discrete surfaces exhibit boundary terms not seen in previous formulae. We also derive error bounds c...

We construct two new families of pseudo-Riemannian manifolds which are curvature homegeneous of type (1, 3). The first family given has signature (2k, 2k + 1) and is curvature homogeneous of type (1, 3) but not curvature homogeneous. The second family given has signature (1, 2) and is curvature homogeneous of type (1, 3) of all orders but not locally homogeneous, showing there is no finite Sing...

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite comple...

Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. Especially, curvature estimation of a mesh is an active research area [GI04, CSM03, CP03] with many applications. The most important curvature measures on a surface are the mean curvature H, the Gaussian curvature K, and the curv...

BACKGROUND Current surgical treatments in Peyronie's disease are accompanied by complications such as penile shortening, loss of sensation, erectile dysfunction and recurrence of disease. The aim of this study was the evaluation of clinical results of intracavernosal plaque excision in Peyronie's disease. METHODS The operation was performed on 35 men. It was consisted of incising the t...