From Symmetry to Monotonicity
Symmetry is a fascinating notion in science, primarily perhaps due to the fact that the symmetry of geometric objects evokes the aesthetic and elegant perception of every human being. More fundamentally, the symmetries of spacetime are closely related to conservation laws in physics. In this note we show how one can use a symmetry of a two-dimensional surface to prove a monotonicity property of a one-dimensional function.
D.K. was partially supported by GACR grant No. 18-08835S and by FCT (Portugal) through project PTDC/MAT-CAL/4334/2014.