Curvature is a key feature in shape analysis and its estimation on discrete simplicial complexes benefits many geometry processing applications. However, its study has mostly remained focused on 2D manifolds and computationally practical extensions to higher dimensions remain an active area of computer science research. We examine the existing notions of distortion, an analog of curvature in th...

We obtain a vanishing theorem for the half-kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base manifold is almost complex, we prove a vanishing theorem for the half-kernel of a spinc Dirac operator twisted by a line bundle with curvature of a mixed ...

Abstract. On the basis of the second gradient operator defined on curved surfaces, the second category of integral theorems for tensor fields, including the second divergence theorems, the second gradient theorems, the second curl theorems and the second circulation theorems, are systematically demonstrated. Simple conservation laws about the mean curvature and Gauss curvature are deduced from ...

Vanadium dioxide (VO2 ) undergoes a thermally induced solid-to-solid phase transition, which can be exploited for actuation purposes. VO2 -coated silicon cantilevers demonstrate abrupt curvature changes when their temperature is varied across the phase transition. Unlike the monotonic hysteresis phenomena observed in many other smart materials, the curvature– temperature hysteresis of VO2 actua...

In [LY] a differential Harnack inequality was proved for solutions to the heat equation on a Riemannian manifold. Inspired by this result, Hamilton first proved trace and matrix Harnack inequalities for the Ricci flow on compact surfaces [H0] and then vastly generalized his own result to all higher dimensions for complete solutions of the Ricci flow with nonnegative curvature operator [ H2]. So...

1 Abstract By using symplectic Majorana spinors as Grassmann coordinates in a superspace associated with the supersymmetric extension of the isometry group on the spherical surface S 2 , it proves possible to formulate supersymmetric models on S 2 using superspace techniques. The formulation of gauge theories on a spherical surface [1] has provided insights into their properties. The kinetic te...

Let (M, g) be a compact Riemannian manifold of dimension N ≥ 5 and Qg be its Q curvature. The prescribed Q curvature problem is concerned with finding metric of constant Q curvature in the conformal class of g. This amounts to finding a positive solution to Pg(u) = cu N+4 N−4 , u > 0 on M where Pg is the Paneitz operator. We show that for dimensions N ≥ 25, the set of all positive solutions to ...

Ridge-like structures in digital images may be extracted by convolving the images with derivatives of Gaussians. The choice of the convolution operator and of the parameters involved defines a specific ridge image. In this paper, various ridge measures related to isophote curvature are constructed, reviewed, and evaluated with respect to their usability in CT/MRI matching of human brain scans. ...

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by L the Laplace–Beltrami operator on M . We assume that the kernel associated to the heat semigroup generated by L satisfies a mild decay condition at infinity. We prove that if m is a bounded holomorphic function in a suitable strip of...