The simple definition of a mean is that of a numeric quantity which represents the center of a collection of numbers. Here the trick lies in defining the exact type of numeric collection, as beyond ...

Harmonic AI, an artificial intelligence startup co-founded by Robinhood Markets Inc. Chief Executive Vlad Tenev, has raised $100 million in funding to tackle a problem that has sometimes confounded AI ...

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 ...

https://doi.org/10.4169/amer.math.monthly.124.6.535 https://www.jstor.org/stable/10.4169/amer.math.monthly.124.6.535 We investigate functions with the property that ...

Biharmonic submanifolds represent an influential area in Riemannian geometry, where the concept of harmonic maps is extended to a fourth-order setting. A submanifold is deemed biharmonic when its ...