We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N = 4 SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a clos...

We first give new estimates for the extrinsic radius of compact hypersurfaces of the Euclidean space R and the open hemisphere in terms of high order mean curvatures. Then we prove pinching results corresponding to theses estimates. We show that under a suitable pinching condition, M is diffeomorphic and almost isometric to an n-dimensional sphere.

We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. In the hyperbolic space, we show that if the volume of M is 1, then there exists a constant C depending on the dimension of M and the L-norm of the second fundamental form B such that the pinching condition tanh(R) < 1 ||H||∞ + C (where H is the mean curvature) implies that M is diffeomorphic to an ...

In this study, we present a calibration technique that is valid for all single-viewpoint catadioptric cameras. We are able to represent the projection of 3D points on a catadioptric image linearly with a 6×10 projection matrix, which uses lifted coordinates for image and 3D points. This projection matrix can be computed with enough number of 3D2D correspondences (minimum 20 points distributed i...

Synonyms – Panoramic camera, spherical camera, catadioptric camera, fisheye camera, wide-angle camera Related Concepts – camera calibration – pinhole camera – radial distortion – omnidirectional vision – camera parameter (intrinsic, extrinsic) – intrinsic parameter matrix – structure from motion – epipolar geometry Definition An omnidirectional camera (from omni, meaning all) is a camera with a...

We present the crumpling transition in three-dimensional Euclidian space of dynamically triangulated random surfaces with edge extrinsic curvature and fixed topology of a sphere as well as simulations of a dynamically triangulated torus. We used longer runs than previous simulations and give new and more accurate estimates of critical exponents. Our data indicate a cusp singularity in the speci...

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N = 4 SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a clos...

We derive and numerically solve a surface active nematodynamics model. validate the numerical approach on sphere analyse influence of hydrodynamics oscillatory motion topological defects. For ellipsoidal surfaces geometric forces these patterns is addressed by taking into account effects intrinsic as well extrinsic curvature contributions. The experiments demonstrate stronger coupling with prop...