Concavity Property of Minimal $$L^2$$ Integrals with Lebesgue Measurable Gain IV: Product of Open Riemann Surfaces

The Riemann and Lebesgue Integrals

§1 Preliminaries: Step Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 §2 Riemann Integrable Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 §3 Lebesgue measure zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 §4 Definition and Properties of the Lebesgue Integral . . . . . . . . . . 7 §5 The spaces L(R) and L(R) ....

Higher genus Riemann minimal surfaces

Even though the classification of genus zero, embedded minimal surfaces is not complete, W. H. Meeks J. Perez and A. Ros [14], [15], [16] have made progress concerning the question of the uniqueness of the Riemann examples in the class of genus zero embedded minimal surfaces which have an infinite number of ends. They conjecture in [15] that every embedded minimal surface of finite genus and wi...

A Property of Minimal Surfaces.

Approximation of Lebesgue Integrals by Riemann Sums and Lattice Points in Domains with Fractal Boundary

Sets thrown at random in space contain, on average, a number of integer points equal to the measure of these sets. We determine the mean square error in the estimate of this number when the sets are homothetic to a domain with fractal boundary. This is related to the problem of approximating Lebesgue integrals by random Riemann sums.

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...