Harmonic maps

Harmonic maps are mathematical functions that connect two shapes or spaces in a way that minimizes twisting and stretching. Imagine smoothly stretching a rubber sheet stretched over a frame so that it fits another shape as naturally as possible. These maps aim to find the most "efficient" way to move from one space to another, often used to study geometric properties and relationships. They have applications in physics, engineering, and computer graphics, helping us understand how different structures can be formed or related in a minimal-energy, balanced manner.