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Bloch and 5 more Interdisciplinary Applied Mathematics Series No. Chen and 2 more Springer Monographs In Mathematics Series. Graduate Texts In Physics Series. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner.

In particular, it can be used as a basis for graduate courses on any of these three subjects.

## Dimension theory of flows: A survey

The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs. He is also the author of more than articles in mathematics, mainly in differential equations and dynamical systems. It is targeted at readers, particularly graduate students, who are familiar with the general theory of measure and integration ….

JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Universitext Free Preview. MR 89f Abramovich and C. An invitation to operator theory, Graduate Studies in Mathematics, vol. MR h On the uniqueness of asymptotic limits of the Ricci flow. MR 56 Adams and J. MR e On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems MR 26 Pure Appl.

MR c Agmon, A.

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Douglis, and L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Dual semigroups and second order linear elliptic boundary value problems MR 85i Linear and quasilinear parabolic problems Monographs in Mathematics, vol. MR 96g Ambrosetti and P. Dual variational methods in critical point theory and applications, J. Functional MR 51 Andrews and C. Mean curvature flow of pinched submanifolds to spheres MR a MR d Angiuli, D.

Pallara, and F. Semigroup Forum,80, Aronszajn, F. Mulla, and P. On spaces of potentials connected with Lp classes MR 31 Annales Inst. Aronszajn and K. Theory of Bessel potentials. I MR 26 Atiyah and R. The Yang-Mills equations over Riemann surfaces, Philos. London Ser. A , MR 85k Construction of Instantons - Atiyah, M. A65 Atiyah, N. Hitchin, and I. Self-duality in four-dimensional Riemannian geometry MR 80d Math Pures Appl. MR 55 Nonlinear analysis on manifolds.

MR 85j Some nonlinear problems in Riemannian geometry Berlin,. Another proof of the Yamabe conjecture for locally conformally flat manifolds MR 94e Nonlinear Anal. Proof of the Yamabe conjecture, without the positive mass theorem, for locally conformally flat manifolds, Einstein metrics and Yang-Mills connections Sanda, , Lecture Notes in Pure and Appl.

MR 94m The mean curvature flow of submanifolds of high codimension, Ph. Banasiak and L. MR i Barbu and T. Convexity and optimization in Banach spaces, fourth ed Monographs in Mathematics Dordrecht,. MR Lecture notes on mean curvature flow, barriers and singular perturbations, Appunti. Benjamini, I. Chavel, and E. Heat kernel lower bounds on Riemannian manifolds using the old ideas of Nash, Proc.

London Math. MR 97c Nonlinearity and functional analysis Press, New York,. MR 58 Berger, P. Gauduchon, and E. MR 43 Bergh and J. Interpolation spaces. Berline, E. Getzler, and M. MR m Hulshof, Energy concentration for 2-dimensional radially symmetric equivariant harmonic map heat flows MR j Einstein manifolds Berlin,. MR 88f The approximation problem for Sobolev maps between two manifolds MR 92f Acta Math. Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions MR Nonlinearity,28, arXiv Bierstone and P. Semianalytic and subanalytic sets, Inst.

Hautes Etudes Sci. Biswas and G. Morse theory for the space of Higgs G-bundles MR c Nonexistence of shrinkers for the harmonic map flow in higher dimensions, Int. Not MR Knot Theory. Partial Boling, C. Kelleher, and J. Entropy, stability, and harmonic map flow. Yang-Mills fields which are not selfdual - Bor, G. Bor and R. SO 3 invariant Yang-Mills fields which are not self-dual, Hamiltonian systems, transformation groups and spectral transform methods Montreal, PQ, , Univ.

MR 92f Berestycki, J-M. Coron, and I. Ekeland eds. Convergence of the Yamabe flow for arbitrary initial energy MR e Convergence of the Yamabe flow in dimension 6 and higher MR k Blow-up phenomena for the Yamabe equation MR m On the conformal scalar curvature equation and related problems, Surveys in differential geometry. Geometric flows, Surv. Press, Somerville, MA,, pp. MR k Evolution equations in Riemannian geometry MR j Brendle and F.

Blow-up phenomena for the Yamabe equation. II MR k Functional analysis, Sobolev spaces and partial differential equations, Universitext New York,. MR a Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents MR 84h Semi-linear second-order elliptic equations in L1 MR 49 On the spectral theory of elliptic differential operators. I, Math.

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MR 35 Hermitian-Einstein connections and stable vector bundles over compact complex surfaces MR 89d Buck and J. A simple energy function for knots MR 95k Topology Appl. Lebesgue spaces of differentiable functions and distributions, Partial differential equations C. Morrey, ed Proc. Pure Math. MR 26 Private communcation, February Cannarsa, B. Terreni, and V. Analytic semigroups generated by nonvariational elliptic systems of second order under Dirichlet boundary conditions MR 87e Cannarsa and V.

Generation of analytic semigroups in the Lp topology by elliptic operators in Rn MR 89h Cao, R. Hamilton, and T. Gaussian densities and stability for some Ricci solitons, arXiv:. Cao and X. Asian J. G Stuttgart,.

## Alberto Pinto

Carlotto, O. Chodosh, and Y. Slowly converging Yamabe flows MR Chang and W. Coron, J-M. Ghidaglia, and F. NATO Adv. C Math. Chang, W. Ding, and R. Finite-time blow-up of the heat flow of harmonic maps from surfaces MR 93h Eigenvalues in Riemannian geometry, Pure and Applied Mathematics, vol. MR 86g Cheeger and D.

Comparison theorems in Riemannian geometry Publishing Co. American Publishing Co. Chen and C-L. MR 96f Monotonicity formula and small action regularity for Yang-Mills flows in higher dimensions, Calc. Partial MR 98c Gordon and Breach. Evolution problem of Yang-Mills flow over 4-dimensional manifold, Variational methods in nonlinear analysis Erice, Basel,, pp.

MR 99g Chen, C-L. Shen, and Q. Asymptotic behavior of Yang-Mills flow in higher dimensions, Differential geometry and related topics, World Sci. Chen and L-C. Second order elliptic equations and elliptic systems, Translations of Mathematical Monographs, vol. MR 99i Stabilities of homothetically shrinking Yang-Mills solitons - Chen, Zhengxiang et al.

On the Lojasiewicz-Simon gradient inequality MR c Jendoubi, ed.. Chill and A. Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations, J MR k Chill, A. Haraux, and M. Applications of the Lojasiewicz-Simon gradient inequality to gradient-like evolution equations, Anal.

Chill and M. Convergence to steady states in asymptotically autonomous semilinear evolution equations MR d Convergence to steady states of solutions of non-autonomous heat equations in RN MR h The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature MR 93d Chow, S. Chu, D. Glickenstein, C.

Guenther, J. Ivey, D. Knopf, P Lu, F. Luo, and L. Ni The Ricci flow: techniques and applications. Part I Mathematical Surveys and Monographs, vol. MR f The Ricci flow: techniques and applications. MR j Chow and D. The Ricci flow: an introduction, Mathematical Surveys and Monographs, vol.

## Dimension Theory of Hyperbolic Flows

Chow, P. Lu, and L.

Colding and W. II, Lojasiewicz inequalities and applications. Surveys Diff. Cwikel and S. Complex interpolation of compact operators: an update, Proc. Estonian Acad. The topology of the space of stable bundles on a compact Riemann surface MR 93i Daskalopoulos and R. Reine Angew. Correction to the paper:. Heat kernels and spectral theory, Cambridge Tracts in Mathematics, vol. De Napoli and I. Elementary proofs of embedding theorems for potential spaces of radial functions. Nonlinear functional analysis -Verlag, Berlin,. MR 86j Denk and M. Resolvent estimates for elliptic systems in function spaces of higher regularity, Electron.

J MR e Denk, M. Hieber, and J.