Minimal surfaces are surfaces that locally minimize ... the existence of infinitely many minimal hypersurfaces in closed Riemannian manifolds of dimensions between 3 and 7, which confirms a ...

In particular, there are no such mappings for the surfaces of the higher genus. This theorem follows the work of ... In 1981, Gromov asked whether there are closed simply connected manifolds of higher ...

Differential manifolds provide higher dimensional generalizations of surfaces. They appear in a very natural manner in many areas of mathematics and physics. On a differential manifold or more ...

Another area of exploration involves Willmore surfaces and Hopf tori within homogeneous three-manifolds. Research has defined a Willmore functional for surfaces immersed in these spaces and ...

Low-dimensional topology, hyperbolic geometry and 3-manifolds, knot theory, contact geometry, curve complex and mapping class group. William Menasco's research has touched several areas in ...

The Vertices'N'Faces structure (VNF) holds the data used by polyhedron() to construct objects: a vertex list and a list of faces. This library makes it easier to construct polyhedra by providing ...

Most beziers are cubic (degree 3). The higher the degree, the more the curve can wiggle. Bezier Patch A two-dimensional arrangement of Bezier control points that generate a bounded curved Bezier ...

A historian looks at Lahore as a case-study to see how his hometown has systematically lost its connection to its many-splendoured Published 02 Feb, 2025 09:17am ...

We’re a week in, and the Trump blitzkrieg has had its desired effect—everyone is stunned by the sweep and depth of the ...