66 citations · 327 across the 22 of their papers we have counts for
5 papers · 1 filter
Searching for the maximal valence of harmonic polynomials: a new example
Seung-Yeop Lee, Andres Saez
We find a new lower bound for the maximal number of zeros to harmonic polynomials, , when and .
Zeros of harmonic polynomials, critical lemniscates and caustics
Dmitry Khavinson, Seung-Yeop Lee, Andres Saez
In this paper we sharpen significantly several known estimates on the maximal number of zeros of complex harmonic polynomials. We also study the relation between the curvature of c…
Sharpness of connectivity bounds for quadrature domains
Seung-Yeop Lee, Nikolai Makarov
In this paper we prove the sharpness of connectivity bounds established in [15]. The proof depends on some facts in the theory of univalent polynomials. We also discuss application…
Remarks on Wilmshurst's theorem
Seung-Yeop Lee, Antonio Lerario, Erik Lundberg
We demonstrate counterexamples to Wilmshurst's conjecture on the valence of harmonic polynomials in the plane, and we conjecture a bound that is linear in the analytic degree for e…
Topology of quadrature domains
Seung-Yeop Lee, Nikolai Makarov
We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in…