0000000000543010

AUTHOR

Haiqing Xu

showing 3 related works from this author

Weighted estimates for diffeomorphic extensions of homeomorphisms

2019

Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$

Pure mathematicsMathematics::Functional AnalysisMathematics - Complex VariablesdiffeomorphismGeneral MathematicsMultiple integralHigh Energy Physics::Phenomenologyinternal chord-arc domainPoisson extensionExtension (predicate logic)OmegafunktioteoriaHomeomorphism (graph theory)Domain (ring theory)FOS: MathematicsDiffeomorphismComplex Variables (math.CV)Mathematics
researchProduct

Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains

2019

AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.

Mathematics::Dynamical SystemsDegree (graph theory)Mathematics - Complex Variables010102 general mathematicsInverseConformal mapType (model theory)01 natural sciencesUnit diskCombinatoricsDistortion (mathematics)inner cuspDifferential geometryCardioid0103 physical sciencesFOS: Mathematicshomeomorphisms of finite distortionanalyyttinen geometria010307 mathematical physicsGeometry and TopologyComplex Variables (math.CV)0101 mathematicsextensionsMathematicsThe Journal of Geometric Analysis
researchProduct

Controlled diffeomorphic extension of homeomorphisms

2018

Let $\Omega$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$ be a homeomorphism. We show that $\varphi$ has finite dyadic energy if and only if $\varphi$ has a diffeomorphic extension $h: \mathbb D\rightarrow \Omega$ which has finite energy.

Mathematics::Functional AnalysisPure mathematicsMathematics::Dynamical SystemsMathematics - Complex VariablesdiffeomorphismApplied Mathematicsta111010102 general mathematicsHigh Energy Physics::PhenomenologyPoisson extensionExtension (predicate logic)01 natural sciencesHomeomorphismfunktioteoria010101 applied mathematicsDomain (ring theory)chord-arc curveFOS: MathematicsDiffeomorphismtopologia0101 mathematicsComplex Variables (math.CV)AnalysisEnergy (signal processing)Mathematics
researchProduct