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As one of most important objects in mathematics, ‘manifold’ has provided us more and more insights and benefits. In the past half century, more and more different areas in mathematics have been inters...
Given the fundamental importance of moduli spaces and their applications in many different topics, we are organizing a week long conference titled "Moduli spaces and applications in geometry, topology...
Abstract: Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy g...
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace theory that play a prominent role in analytic approaches to symplectic topology. These include relations...
For each k > 0 we find an explicit function fk such that the topology of S inside the ball BS(p, r) is ‘bounded’ by fk(r) for every complete Riemannian surface (compact or noncompact) S with K  W...

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