"Welcome to the inaugural issue of College Mathematics. This collection represents the bridge we aim to build between inquiry and rigor. In this issue, we explore topics ranging from analytic number theory to novel pedagogical approaches in calculus."
We give explicit counterexamples to two questions. One is asked by Pogorelov and the other is by Toponogov, at least both are stated in. These questions concern the existence of closed asymptotic curves in a saddle surface, namely a complete immersed regular surface in R^3 with nonpositive Gaussian/sectional curvature, and its geometric consequences under some topological conditions. We also modify the statements and prove a corrected version. In the appendix we include an example clarifying a conjecture of Milnor.
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