L4A 1.Theorem: A Compact Surface Has an Elliptic Point L4B 1.Theorem: A Compact Connected Surface with Constant Gauss Curvature Is a Sphere 2.Lemma: Three Conditions of a Point to Be an Umbilical Point 3.Proof: A Compact Connected Surface with Constant Gauss Curvature Is a Sphere L4C 1.Proof: A Compact Connected Surface with Constant Gauss Curvature Is a Sphere (cont.) 2.Proof: Three Conditions of a Point to Be an Umbilical Point