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Currently displaying 1 – 2 of 2

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The local structure of Nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds.

Jingyi Chen — 1994

Manuscripta mathematica

Quaternionic maps and minimal surfaces

Jingyi Chen; Jiayu Li — 2005

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $(M, J^{α}, α = 1, 2, 3)$ and $(N, 𝒥^{α}, α = 1, 2, 3)$ be hyperkähler manifolds. We study stationary quaternionic maps between $M$ and $N$ . We first show that if there are no holomorphic 2-spheres in the target then any sequence of stationary quaternionic maps with bounded energy subconverges to a stationary quaternionic map strongly in $W^{1, 2} (M, N)$ . We then find that certain tangent maps of quaternionic maps give rise to an interesting minimal 2-sphere. At last we construct a stationary quaternionic map with a codimension-3 singular set by using the embedded...

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