International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2020-01-11 , DOI: 10.1093/imrn/rnz348
Jung J, Zelditch S.

We show that real and imaginary parts of equivariant spherical harmonics on ${{\mathbb{S}}}^3$ have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is $N$ and the equivariance degree is $m$, then the expected genus is proportional to $m \left (\frac{N^2 - m^2}{2} + N\right )$. Hence, if $\frac{m}{N}= c$ for fixed $0 < c < 1$, then the genus has order $N^3$.

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