On the surface integral and Gauss-Green’s theorem

The Gauss-Bonnet Theorem

Remarks on the Gauss-Green Theorem

These notes cover material related to the Gauss-Green theorem that was developed for work with S. Hofmann and M. Mitrea, which appeared in [HMT].

The Gauss-bonnet Theorem

The Gauss Bonnet theorem links differential geometry with topology. The following expository piece presents a proof of this theorem, building up all of the necessary topological tools. Important applications of this theorem are discussed.

Integral Geometry and the Gauss-bonnet Theorem in Constant Curvature Spaces

We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.

The Gauss-lucas Theorem and Jensen Polynomials

A characterization is given of the sequences {"fyj^o vvith the property that, for any complex polynomial/(z) = 1akzk and convex region Kcontaining the origin and the zeros of/, the zeros of 2 y¡<akzk again lie in K. Many applications and related results are also given. This work leads to a study of the Taylor coefficients of entire functions of type I in the Laguerre-Pólya class. If the power s...