# American Institute of Mathematical Sciences

April  2005, 12(3): 377-385. doi: 10.3934/dcds.2005.12.377

## On the regularity of integrable conformal structures invariant under Anosov systems

 1 Department of Mathematics, 1 University Station C1200, University of Texas, Austin, TX 78712, United States 2 Department of Mathematics and Statistics, ILB 325, University of South Alabama, Mobile, AL 36688, United States

Received  October 2003 Revised  August 2004 Published  December 2004

We consider conformal structures invariant under a volume-preserving Anosov system. We show that if such a structure is in $L^p$ for sufficiently large $p$, then it is continuous.
Citation: Rafael De La Llave, Victoria Sadovskaya. On the regularity of integrable conformal structures invariant under Anosov systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 377-385. doi: 10.3934/dcds.2005.12.377
 [1] Domenico Mucci. Maps into projective spaces: Liquid crystal and conformal energies. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 597-635. doi: 10.3934/dcdsb.2012.17.597 [2] Haim Brezis, Petru Mironescu. Composition in fractional Sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 241-246. doi: 10.3934/dcds.2001.7.241 [3] Tahar Z. Boulmezaoud, Amel Kourta. Some identities on weighted Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 427-434. doi: 10.3934/dcdss.2012.5.427 [4] Daniel Guan. Classification of compact homogeneous spaces with invariant symplectic structures. Electronic Research Announcements, 1997, 3: 52-54. [5] Tomasz Szarek, Mariusz Urbański, Anna Zdunik. Continuity of Hausdorff measure for conformal dynamical systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4647-4692. doi: 10.3934/dcds.2013.33.4647 [6] Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 627-650. doi: 10.3934/dcds.2009.25.627 [7] Huyi Hu, Miaohua Jiang, Yunping Jiang. Infimum of the metric entropy of volume preserving Anosov systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4767-4783. doi: 10.3934/dcds.2017205 [8] Patrick Foulon, Boris Hasselblatt. Lipschitz continuous invariant forms for algebraic Anosov systems. Journal of Modern Dynamics, 2010, 4 (3) : 571-584. doi: 10.3934/jmd.2010.4.571 [9] Alexandre B. Simas, Fábio J. Valentim. $W$-Sobolev spaces: Higher order and regularity. Communications on Pure & Applied Analysis, 2015, 14 (2) : 597-607. doi: 10.3934/cpaa.2015.14.597 [10] Shiping Cao, Shuangping Li, Robert S. Strichartz, Prem Talwai. A trace theorem for Sobolev spaces on the Sierpinski gasket. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3901-3916. doi: 10.3934/cpaa.2020159 [11] Younghun Hong, Yannick Sire. On Fractional Schrödinger Equations in sobolev spaces. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2265-2282. doi: 10.3934/cpaa.2015.14.2265 [12] Ruiqi Jiang, Youde Wang, Jun Yang. Vortex structures for some geometric flows from pseudo-Euclidean spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1745-1777. doi: 10.3934/dcds.2019076 [13] Ünver Çiftçi. Leibniz-Dirac structures and nonconservative systems with constraints. Journal of Geometric Mechanics, 2013, 5 (2) : 167-183. doi: 10.3934/jgm.2013.5.167 [14] Yanfang Peng. On elliptic systems with Sobolev critical exponent. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3357-3373. doi: 10.3934/dcds.2016.36.3357 [15] Irena Lasiecka, Buddhika Priyasad, Roberto Triggiani. Uniform stabilization of Boussinesq systems in critical $\mathbf{L}^q$-based Sobolev and Besov spaces by finite dimensional interior localized feedback controls. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 4071-4117. doi: 10.3934/dcdsb.2020187 [16] Vy Khoi Le. On the existence of nontrivial solutions of inequalities in Orlicz-Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 809-818. doi: 10.3934/dcdss.2012.5.809 [17] Duchao Liu, Beibei Wang, Peihao Zhao. On the trace regularity results of Musielak-Orlicz-Sobolev spaces in a bounded domain. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1643-1659. doi: 10.3934/cpaa.2016018 [18] Haruki Umakoshi. A semilinear heat equation with initial data in negative Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020365 [19] Laurent Amour, Jérémy Faupin. Inverse spectral results in Sobolev spaces for the AKNS operator with partial informations on the potentials. Inverse Problems & Imaging, 2013, 7 (4) : 1115-1122. doi: 10.3934/ipi.2013.7.1115 [20] Rowan Killip, Satoshi Masaki, Jason Murphy, Monica Visan. The radial mass-subcritical NLS in negative order Sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 553-583. doi: 10.3934/dcds.2019023

2019 Impact Factor: 1.338