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As it is mentioned by Deane Yang in Ricci flow preserves locally symmetry along the flow, we know the local symmetry is preserved under the Ricci flow on the compact manifold since we have the ...

I am looking for an extended version of the implicit/inverse function theorem that would show uniqueness of a strictly increasing implicit function, even when the derivative condition is violated (e.g....

I am researching for the existence and uniqueness of solutions for the equation in figure below enter image description here $$\nabla\cdot u = \frac{\dot b(t)}{b(t)} \text{ in }\Omega(t) \tag{1}$$ The ...