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What is this course about? The foundations of di erential geometry (=
study of manifolds) rely on analysis in several variables as \local machinery": many
global theorems about manifolds are reduced...
Nothing found here is original except for a few mistakes and misprints here and there. These notes are simply a record of what I cover in class, to spare the students the necessity of taking the lectu...
Addendum to "Energies of zeros of random sections on Riemann surfaces" [arXiv:0705.2000]. Indiana Univ. Math. J. 57 (2008), no. 4, 1753-1780
Energies of zeros of random sections Riemann surfaces
2010/12/9
The purpose of this note is to resolve an apparent discrepancy between the calculations
in the article [ABS] of Armentano- Beltran-Shub (henceforth ABS) and that in Qi Zhong’s
article [Zh] of the as...
Comments on: "Optical solitons in a parabolic law media with fourth order dispersion"[Appl. Math. Comput. 208(2009)209-302]
Optical solitons parabolic law media fourth order dispersion
2010/4/6
Biswas and Milovic[Appl. Math. Comput.208(2009)209-302] have found the optical one-soliton solutions of a fourth order dispersive cubic-quintic nonlinear Schr\"odinger equation. In this comment, we fi...
Differential Forms and the Noncommutative Residue for Manifolds with Boundary II non-product metric case(to appear in Lett. Math. Phys.)(amend on 2-23-2006)
Noncommutative residue for manifolds with boundary non-product metric conformal invariant
2018/4/20
In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to deˉne a conformal invariant pair. For a 4...