Ever since the ancient Greeks first made observations of the circular Moon and the skies, scientists have known that the Earth is a sphere. We’ve all seen beautiful images of the Earth from space, ...

Scientific proof that Earth is round (and how to explain it) To put it bluntly, we know more about the curvature of Earth than almost any other topic in the realm of physical science. There are ...

A Universe with too much matter-and-energy for its expansion rate will have positive curvature, while one with too little will have negative curvature. Only the perfectly balanced case will be flat.

All other cosmological data suggests the universe is flat, meaning it has no curvature, similar to a sheet of paper. These Planck measurements indicate that it could be “closed”, or spherical ...

To this end we focus on the mean curvature flow of a topological annulus with inner boundary meeting a standard 𝑛-sphere in ℝ𝑛⁺¹ perpendicularly and outer boundary fixed to an (𝑛 − 1)-sphere with ...

Abstract: Let (M,g) be a four-dimensional closed connected oriented (possibly non-spin) Riemannian manifold with scalar curvature bounded below by 12. We prove that, if f is a smooth distance ...