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A proof of Thurston's topological characterization of rational functions
Thurston's topological characterization rational functions
2015/8/26
The criterion proved in this paper was stated by Thurston in November 1982. Thurston lectured on its proof on several occasions, notably at the NSF summer conference inDuluth, 1983, where one of the a...
Spaces of measurable functions
measurable functions absolute retracts infinite-dimensional manifolds reflective isotopy property Z-sets
2011/8/29
Abstract: For a metrizable space $X$ and a finite measure space $(\Omega,\mathfrak{M},\mu)$ let $M_{\mu}(X)$ and $M^f_{\mu}(X)$ be the spaces of all equivalence classes (under the relation of equality...
On the topology of semi-algebraic functions on closed semi-algebraic sets
topology of semi-algebraic functions closed semi-algebraic sets
2011/1/20
We consider a closed semi-algebraic set X Rn and a C2 semi-algebraic function f : Rn ! R such that f|X has a finite number of critical points. We relate the topology of X to the topology of the sets...
Green functions, the fine topology and restoring coverings
Harmonic measure Jensen measures Subharmonic functions
2011/2/22
There are several equivalent ways to define continuous harmonic functions H(K) on a compact set K in Rn. One may let H(K) be the unform closures of all functions in C(K) which are restrictions of harm...
Notes on Certain Subclass of $p$-Valently Bazilevič Functions
Analytic functions Multivalent functions Bazilevi{c} functions subordination between analytic functions Briot-Bouquet differential subordination
2010/1/22
In the present paper, we discuss a subclass of -valently Bazilevic functions, which was introduced and investigated recently by Patel [5]. Such results as inclusion relationship, coefficient inequal...
TOPOLOGICAL STRING PARTITION FUNCTIONS AS EQUIVARIANT INDICES
TOPOLOGICAL STRING PARTITION FUNCTIONS EQUIVARIANT INDICES
2018/4/20
We propose to use the identiˉcation of topological string partition functions as equivariant indices on framed moduli spaces of instantons to study the Gopakumar-Vafa conjecture for some local Calabi-...