Motivated by the strong maximum principle for Paneitz operator in dimension 5 or higher found in [GM] and the calculation of the second variation of the Green’s function pole’s value on S3 in [HY2], we study Riemannian metric on 3 manifolds with positive scalar and Q curvature. Among other things, we show it is always possible to …nd a constant Q curvature metric in the conformal class. Moreove...

We consider the entropy problem of AdS3 black holes using the conformal field theory at the horizon. We observe that the supersymmetry is enhanced at the horizon of massless AdS3 black hole. This allows us to determine the vacuum of the modular invariant conformal field theory to be the NS-ground state (which corresponds to AdS3 spacetime). This is smoothly related to the R-ground state (corres...

The dispersion in an eccentric annulus region by taking blood as a Newtonian fluid with the investigation of oxygen transfer to the tissue cells in an eccentric catheterized artery is studied. The region bounded by eccentric circles in x-y plane is conformal mapping to concentric circles in   plane using a conformal mapping 1 . z c    The resulting governing equations are analytically solv...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

We present the theory of a two-dimensional conformal scalar field using path integral techniques. We derive the conformal anomaly using an adaptation of the method of Fujikawa, and compare the result with a derivation based on a Pauli-Villars measure, where the anomaly is shifted from the path integral measure to the energy-momentum trace. In the path integral approach the energy-momentum is a ...