We show that Carathéodory's conjecture on umbilical points of closed convex surfaces may be reformulated in terms of the existence of at least one umbilical point in the graphs of functions f: R 2 → R ...

We extend the classical existence and uniqueness theory of Jenkins-Serrin (H = 0) and Spruck (H > 0) for the constant mean curvature equation over a domain in R², to domains in H² or S². This theory ...

Try matching the following graphs with their corresponding function types: A periodic wave that oscillates between -1 and 1.

Left graph follows the conventional approach of plotting the energy spectrum, E(k), where energy is a is distributed across ...