Kenneth Falconer - Books, Papers, Preprints
Links to listingsMathSciNet
BooksThe Geometry of Fractal Sets, Cambridge UP, 1985; paperback 1986.
Fractal Geometry - Mathematical Foundations and Applications , John Wiley, Third Edition, 2014, with Solutions Manual 3rd Ed.
Unsolved Problems in Geometry (with H.T. Croft and R.K. Guy), Springer-Verlag, 1991.
Techniques in Fractal Geometry, John Wiley, 1997.
Fractals - A Very Short Introduction, Oxford UP, 2013.
Some selected papersThe Hausdorff dimension of self-affine fractals, Math. Proc. Cambridge Philos. Soc., 103 (1988), 339-350.
The dimension of self-affine fractals II, Math. Proc. Cambridge Philos. Soc., 111 (1992), 169-179.
Bounded distortion and dimension for non-conformal repellers, Math. Proc. Cambridge Philos. Soc. 115 (1994) 315-334.
The multifractal spectrum of statistically self-similar measures, J. Theoretical Probability, 7 (1994) 681-702.
Probabilistic methods in fractal geometry, Proc. Conf. Fractal Geometry and Stochastics, Finsterbergen 1994, Progress in Probability, 37 (1995), 3-13.
(with P. Mattila) The packing dimension of projections and sections of measures, Math. Proc. Cambridge Philos. Soc., 119 (1996), 695-713.
(with T.C. O'Neil) Vector-valued multifractal measures, Proc. Royal. Soc. Ser. A: Math and Phys. Sci., 452 (1996), 1433-1457.
(with J.D. Howroyd) Packing dimensions of projections and dimension profiles, Math. Proc. Cambridge Philos. Soc., 121 (1997), 269-286.
(with B. Lammering) Fractal properties of generalized Sierpinski triangles, Fractals,6 (1998), 31-41.
(with M Järvenpää) Packing dimensions of sections of sets, Math. Proc. Cambridge Philos. Soc., 125(1999), 89-104.
Generalised dimensions of measures on self-affine sets, Nonlinearity, 12(1999), 877-891.
Semilinear PDEs on self-similar fractals, Commun. Math. Phys. 206(1999), 235-245.
A nonlinear Mercerian theorem, J. Math. Anal. App. 239(1999), 440-448.
Representation of families of sets by measures, multifractal analysis and Diophantine approximation, Math. Proc. Cambridge Philos. Soc. 128(2000), 111-121.
(with J. Lévy Véhel) Horizons of fractional Brownian surfaces, Proc. Roy. Soc. London, Ser. A. 456(2000), 2153--2177
(with M. Järvenpää and P. Mattila) Examples illustrating the instability of packing dimensions of sections, Real Analysis Exchange, 25 (2000), 629--640.
(with R.D. Mauldin) Fubini-type theorems for general measure constructions, Mathematika, 47 (2000), 251--265.
(with J. Hu) Nonlinear diffusion equations on unbounded fractal domains, J. Math. Anal. App., 256(2001), 606--624.
Tangent fields and the local structure of random fields, J. Theoret. Probab. 15 (2002), 731--750.
The local structure of random processes, J. London Math. Soc.67 (2003), 657--672.
One-sided multifractal analysis and points of non-differentiability of devil's staircases, Math. Proc. Cambridge Philos. Soc. 136 (2004), 167-174.
Dimensions of intersections and distance sets for polyhedral norms; Real Analysis Exchange, 30(2005),719--726.
(with J. O'Connor) Symmetry and enumeration of self-similar fractals; Bull. London Math. Soc., 39 (2007), 272-282.
(with C. Fernández) Inference on fractal processes using multiresolution approximation; Biometrika, 94 (2007), 313-334. Preprint
(with Y. Demichel) The Hausdorff dimension of pulse-sum graphs; Math. Proc. Cambridge Philos. Soc., 143 (2007), 145-155. Preprint
(with J. Miao) Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices; Fractals, 15 (2007), 289-299. Preprint
(with R. Le Guével and J. Lévy Véhel) Localisable moving average stable and multistable processes, Stochastic Models, 25 (2009), 648-672. arXiv
(with A. Sloan) Continuity of subadditive pressure for self-affine sets, Real Analysis Exchange, 34 (2009), 413-428. Preprint
(with J.M. Fraser) The horizon problem for prevalent surfaces, Math. Proc. Cambridge Philos. Soc., 151 (2011), 355-372 , arXiv
(with Jiaxin Hu and Yuhua Sun) Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh A Mathematics 142 (2012), 1003-1025 , arXiv
(with G.C. Boore) Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure, Math. Proc. Cambridge Philos. Soc. 154 (2013), 325-349
(with Xiong Jin) Dimension conservation for self-similar sets and fractal percolation, Int. Math. Res. Notices, 2015(24) (2015), 13260-13289, arXiv
(with J.M. Fraser and Xiong Jin) Sixty years of fractal projections, in Fractal Geometry and Stochastics V, Progress in Probability 70, pp.3-25, Birkhauser (2015), arXiv
From fractional Brownian motion to multifractional and multistable motion, in Benoit Mandelbrot - A Life in Many Dimensions, pp.239-256, World Scientific, 2015
(with Tom Kempton) The dimension of projections of self-affine sets and measures, Annales Academiae Scientiarum Fennicae - Mathematica 42 (2017), 473-486, arXiv
(with Tom Kempton) Planar self-affine sets with equal Hausdorff, box and affinity dimensions, Ergodic Theory and Dynamical Systems 38 (2018), 1289-1341, arXiv
A capacity approach to box and packing dimensions of projections and other images, arXiv
A capacity approach to box and packing dimensions of projections of sets and exceptional directions, to appear, J. Fractal Geometry. arXiv