geometric analysis

Geometric analysis is a branch of mathematics that explores the relationship between shapes, spaces, and their properties using tools from calculus and differential equations. It examines how curved surfaces and volumes behave, how they can be measured, and how functions can be studied on these geometric objects. This field helps us understand complex structures in nature, physics, and engineering, such as the shape of the universe, the behavior of materials, or the flow of fluids. Overall, it combines geometry's visual intuition with analysis's precision to analyze the fundamental properties of shapes and spaces.