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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Prof. Xiaoping Yang,Nanjing University

Inviter: 李竞 研究员
Title:
Upper Measure Bounds of Nodal Sets of Solutions to the Bi-Harmonic Equations on C^\infty Riemannian Manifoldse
Time & Venue:
2018.12.21 9:00 N613
Abstract:

In this talk, we discuss the nodal set of a bi-harmonic function u on an n-dimensional $C^\infty$ Riemannian manifold $M.$ We first define the frequency function and the doubling index for the bi-harmonic function u, and then establish their monotonicity formulae and doubling conditions. With the help of establishing the smallness propagation and partitions for u, we show that, for some ball, an upper bound for the measure of nodal set of the biharmonic function u can be controlled by $N^\alpha$. Among others, we also show that the n-1 dimensional Hausdordff measures of nodal sets of such solutions are bounded by the frequency function, which is independently interesting. This is a joint work with Tian Long.

 

 

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