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We study the Eisenstein series for GL(3,Z) induced from cusp forms. We give the expression of the Fourier-Whittaker coefficients of the Eisenstein series in terms of the Jacquet integrals. Moreover, by evaluating the Jacquet integrals, we give the Mellin-Barnes type integral expressions of those...
Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten invariants defined using exploded manifolds or log schemes....
The Kelmans-Seymour conjecture states that every 5-connected nonplanar graph contains a subdivided K
5. Certain questions of Mader propose a “plan” towards a possible resolution of this conjecture. One part of this plan is to show that every 5-connected nonplanar graph containing
Improving a result of Eschenburg and Kim we give a criterion for semisimplicity of pseudo-Riemannian extrinsic symmetric spaces in terms of the shape operator with respect to the mean curvature vector.
We show that a solution to graphical mean curvature flow with a perpendicular boundary condition over a convex domain in Minkowski space exists for all time. We additionally show that this solution will converge to a hyperplane as t→∞.
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