Summary
Among all shapes that enclose a given volume, which ones have the smallest possible surface area? This classical question, known as the isoperimetric problem, dates back to ancient Greece and appears naturally in phenomena such as soap bubbles, crystals, and models of the universe in physics. This project aims to deepen our understanding of how geometric properties of a space -- especially curvature -- influence solutions to geometric optimization problems. The broader impact of the project includes mentoring undergraduate and graduate students and organizing seminars to engage the local mathe
