On umbilic points on newly Born surfaces (Q1691487)

The authors show that newly born surfaces in 3-space have 4 and only 4 umbilic points. Umbilics are points on a surface where the curvature is the same in any direction. That is, locally, the surface is spherical. Here, a newly born surface is characterized as a surface created from a function with Morse singularity of index either 0 or 3. In addition to the main proof, the authors further show all 4 umbilic points are of lemon type.