Biharmonic maps extend the concept of harmonic maps by exploring critical points of higher order energy functionals. In Riemannian geometry, while harmonic maps minimise the classical energy ...

Eigenvalue problems occupy a central role in Riemannian geometry, providing profound insights into the interplay between geometry and analysis. At their core, these problems involve the study of ...

The regularity of optimal routes on sub-Riemannian manifolds has been an important open problem in sub-Riemannian geometry since the early 90s. A researcher now gives new restrictions on the shape of ...

It is known that Albert Einstein constructed equations of general relativity by adopting Riemann geometry. In addition to the key role it played in mathematics and physics, Riemann geometry has ...

This is a preview. Log in through your library . Abstract The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the ...

This monthly journal, published since 1900, is devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American ...

WHEN Andrew Wiles, a British mathematician working at Princeton University, announced a decade ago that he had solved Fermat's last theorem, his discovery was reported on front pages around the world.