Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

Einstein's 1917 paper, "Cosmological Considerations in the General Theory of Relativity," applied general relativity to the universe as a whole, establishing a firmer basis for cosmology. To create a ...

Curvature equations lie at the heart of differential geometry and the analysis of hypersurfaces, providing a rigorous framework for understanding the intrinsic and extrinsic geometric properties of ...

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called crossratio equation with a similarity ...

Jason Lotay explains how mathematicians studying special geometries are collaborating with physicists to explore M-theory, an 11-dimensional description of the world that unifies the various string ...

Earlier this year, Mathematician Ian Stewart came out with an excellent and deeply researched book titled "In Pursuit of the Unknown: 17 Equations That Changed the World" that takes a look at the most ...

Geometric partial differential equations of level-set form are usually constructed by a variational method using either Dirac delta function or co-area formula in the energy functional to be minimized ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

In his scientific bestseller, A Brief History of Time, Stephen Hawking remarked that every equation he included would halve sales of the book, so he put only one in it, Einstein's equation relating ...