3 papers
math.DG2026
On questions of Pogorelov and Toponogov
Lei Ni, Wei Zhang, Yijian Zhang
We give explicit counterexamples to two questions. One is asked by Pogorelov and the other is by Toponogov. These questions concern the existence of closed asymptotic curves in a s…
math.DG2026
Dynamics of the Morse vector field
Yijian Zhang
The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of t…
math.DG2026
Universality of the Divergence
Lei Ni, Yijian Zhang
Algebraists asked whether or not an operator on the module of smooth sections of the tangent bundle over the commutative ring of smooth functions of a smooth (orientable) manifold…