Michel Zinsmeister
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Michel Zinsmeister has a total of 21 co-authors. Here are the top co-authors by number of shared publications:
- Yong Han
Shenzhen University China
5 shared publications - Bertrand Duplantier
Institut de Physique Théorique, CEA/Saclay
4 shared publications Huaying Wei
Jiangsu Normal Univ, Dept Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China
4 shared publications- Bertrand Duplantier
Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, Gif-sur-Yvette, France
3 shared publications - Chi Nguyen
Department of Information Technology, Ho Chi Minh University of Transport, Ho Chi Minh City, Vietnam
3 shared publications - Yuefei Wang
School of Mathematical Sciences, Shenzhen University, Shenzhen, China
3 shared publications
Latest Publications
- 6 July 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (8) , 255
Denjoy Domains and BMOA
- 6 July 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (8) , 255
Denjoy Domains and BMOA
- Open Access
Cauchy Integral, Fractional Sobolev Spaces and Chord-Arc Curves
Let $Γ$ be a bounded Jordan curve and $Ω_i,Ω_e$ its two complementary components. For $s\in(0,1)$ we define $\mathcal{H}^s(Γ)$ as the set of functions $f:Γ\to \mathbb C$ having harmonic extension $u$ in $Ω_i\cup Ω_e$ such that $$ \iint_{Ω_i\cup Ω_e} |\nabla u(z)|^2 d(z,Γ)^{1-2s} dxdy<+\infty.$$ If $Γ$ is further assumed to be rectifiable we define $H^s(Γ)$ as the space of measurable functions $f:Γ\to \mathbb C$ such that $$\iint_{Γ\times Γ}\frac{|f(z)-f(ζ)|^2}{|z-ζ|^{1+2s}} dσ(z)dσ(ζ)<+\infty.$$ When $Γ$ is the unit circle these two spaces coincide with the homogeneous fractional Sobolev space defined via Fourier series. For a general rectifiable curve these two spaces need not coincide and our first goal is to investigate the cases of equality: while the chord-arc property is the necessary and sufficient condition for equality in the classical case of $s=1/2$, this is no longer the case for general $s\in (0,1)$. We show however that equality holds for Lipschitz curves. The second goal involves the Plemelj-Calderón problem. ......Open AccessCauchy Integral, Fractional Sobolev Spaces and Chord-Arc Curves
Let $Γ$ be a bounded Jordan curve and $Ω_i,Ω_e$ its two complementary components. For $s\in(0,1)$ we define $\mathcal{H}^s(Γ)$ as the set of functions $f:Γ\to \mathbb C$ having harmonic extension $u$ in $Ω_i\cup Ω_e$ such that $$ \iint_{Ω_i\cup Ω_e} |\nabla u(z)|^2 d(z,Γ)^{1-2s} dxdy<+\infty.$$ If $Γ$ is further assumed to be rectifiable we define $H^s(Γ)$ as the space of measurable functions $f:Γ\to \mathbb C$ such that $$\iint_{Γ\times Γ}\frac{|f(z)-f(ζ)|^2}{|z-ζ|^{1+2s}} dσ(z)dσ(ζ)<+\infty.$$ When $Γ$ is the unit circle these two spaces coincide with the homogeneous fractional Sobolev space defined via Fourier series. For a general rectifiable curve these two spaces need not coincide and our first goal is to investigate the cases of equality: while the chord-arc property is the necessary and sufficient condition for equality in the classical case of $s=1/2$, this is no longer the case for general $s\in (0,1)$. We show however that equality holds for Lipschitz curves. The second goal involves the Plemelj-Calderón problem. ...... - 20 July 2024
- Published by Springer Nature in Mathematische Annalen
- Vol. 391 (1) , 1045-1064
Dirichlet spaces over chord-arc domains
- 20 July 2024
- Published by Springer Nature in Mathematische Annalen
- Vol. 391 (1) , 1045-1064
Dirichlet spaces over chord-arc domains
- Open Access
Denjoy Domains and BMOA
A Denjoy domain is a plane domain whose complement is a closed subset $E$ of the extended real line $\bar{R}$ containing $\infty$ : such a domain is called Carleson-homogeneous if there exists $C>0$ such that for all $z\in E$ and $r>0$, one has $\vert E\cap [z-r,z+r]\vert\geq Cr$, where $\vert\cdot\vert$ is the Lebesgue measure on the line. We prove that if $U=\bar{ \mathbb C}\backslash K$ is a Carleson-homogeneous Denjoy domain then, if $f$ stands for one of its universal coverings, $\log {f'}\in BMOA.$ In order to prove this result, we develop ideas from [On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups, Ann. Fenn. Math. 46(2021),67-77] leading to a general theorem about planar domains giving sufficient conditions ensuring that $\log {f'}\in BMOA$ for any universal covering $f.$Open AccessDenjoy Domains and BMOA
A Denjoy domain is a plane domain whose complement is a closed subset $E$ of the extended real line $\bar{R}$ containing $\infty$ : such a domain is called Carleson-homogeneous if there exists $C>0$ such that for all $z\in E$ and $r>0$, one has $\vert E\cap [z-r,z+r]\vert\geq Cr$, where $\vert\cdot\vert$ is the Lebesgue measure on the line. We prove that if $U=\bar{ \mathbb C}\backslash K$ is a Carleson-homogeneous Denjoy domain then, if $f$ stands for one of its universal coverings, $\log {f'}\in BMOA.$ In order to prove this result, we develop ideas from [On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups, Ann. Fenn. Math. 46(2021),67-77] leading to a general theorem about planar domains giving sufficient conditions ensuring that $\log {f'}\in BMOA$ for any universal covering $f.$ - 30 April 2023
- Published by Springer Nature in Annales Henri Poincare
- Vol. 25 (1) , 425-479
Complex Generalized Integral Means Spectrum of Drifted Whole-Plane SLE and LLE
- 30 April 2023
- Published by Springer Nature in Annales Henri Poincare
- Vol. 25 (1) , 425-479
Complex Generalized Integral Means Spectrum of Drifted Whole-Plane SLE and LLE
- Open Access
Complex Generalized Integral Means Spectrum of Drifted Whole-Plane SLE and LLE
We present new results for the complex generalized integral means spectrum for two kinds of whole-plane Loewner evolutions driven by L\'evy processes: - L\'evy processes with continuous trajectories, which correspond to Schramm-Loewner evolutions (SLE) with a drift term in the Brownian driving function. A natural path to access the standard integral means spectrum in the presence of drift goes through the introduction of the complex generalized integral means spectrum, which is obtained via the so-called Liouville quantum gravity. -Symmetric L\'evy processes for which we generalize recent results by Loutsenko and Yermolayeva.
Open AccessComplex Generalized Integral Means Spectrum of Drifted Whole-Plane SLE and LLE
We present new results for the complex generalized integral means spectrum for two kinds of whole-plane Loewner evolutions driven by L\'evy processes: - L\'evy processes with continuous trajectories, which correspond to Schramm-Loewner evolutions (SLE) with a drift term in the Brownian driving function. A natural path to access the standard integral means spectrum in the presence of drift goes through the introduction of the complex generalized integral means spectrum, which is obtained via the so-called Liouville quantum gravity. -Symmetric L\'evy processes for which we generalize recent results by Loutsenko and Yermolayeva.
- 16 July 2019
- Published by Springer Nature in Science China Mathematics
- Vol. 63 (6) , 1057-1064
Ahlfors-regular curves and Carleson measures
- 16 July 2019
- Published by Springer Nature in Science China Mathematics
- Vol. 63 (6) , 1057-1064
Ahlfors-regular curves and Carleson measures
- 21 March 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 175 (5) , 987-1005
On The Brownian Loop Measure
- 21 March 2019
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 175 (5) , 987-1005
On The Brownian Loop Measure
- 1 August 2018
- Published by Finnish Mathematical Society in Annales Academiae Scientiarum Fennicae Mathematica
- Vol. 43, 669-683
Carleson measures and chord-arc curves
- 1 August 2018
- Published by Finnish Mathematical Society in Annales Academiae Scientiarum Fennicae Mathematica
- Vol. 43, 669-683
Carleson measures and chord-arc curves
- Open Access
Ahlfors-regular curves and Carleson measures
We study the relation between the boundary of a simply connected domain being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk onto the domain. As an application, we characterize the chord-arc curve with small norm and the asymptotically smooth curve in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.
Open AccessAhlfors-regular curves and Carleson measures
We study the relation between the boundary of a simply connected domain being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk onto the domain. As an application, we characterize the chord-arc curve with small norm and the asymptotically smooth curve in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.