The study of quantum ergodicity and the precise estimation of eigenfunctions on Riemannian manifolds lies at the intersection of geometric analysis and quantum physics. In settings where the ...

Eigenvalue problems on Riemannian manifolds lie at the heart of modern geometric analysis, bridging the gap between differential geometry and partial differential equations. In this framework, the ...

While artificial intelligence (AI) has made remarkable achievements in domains like image recognition and natural language processing, it encounters fundamental challenges when trying to deal with ...

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 ...

Abstract In this note we discuss the problem of finding an upper bound on the length of the shortest closed geodesic in a closed Riemannian 3-manifold in terms of the volume. More precisely, we show ...

Riemannian manifolds or geodesic metric spaces of finite or infinite dimension occur in many areas of mathematics. We are interested in the interplay between their local geometry and global ...