Distortion of Dimension under Quasiconformal Mappings

Quasiconformal mappings are natural generalizations of conformal mappings. They are homeomorphisms with 'bounded distortion' of which there exist several approaches. In this work we study dimension distortion properties of quasiconformal mappings both in the plane and in higher dimensional Euclidean setting. The thesis consists of a summary and three research articles. A basic property of quasiconformal mappings is the local Hölder continuity. It has long been conjectured that this regularity holds at the Sobolev level (Gehring's higher integrabilty conjecture). Optimal regularity would also provide sharp bounds for the distortion of Hausdorff dimension. The higher integrability conjecture was solved in the plane by Astala in 1994 and it is still open in higher dimensions. Thus in the plane we have a precise description how Hausdorff dimension changes under quasiconformal deformations for general sets. The first two articles contribute to two remaining issues in the planar theory. The first one concerns distortion of more special sets, for rectifiable sets we expect improved bounds to hold. The second issue consists of understanding distortion of dimension on a finer level, namely on the level of Hausdorff measures. In the third article we study flatness properties of quasiconformal images of spheres in a quantitative way. These also lead to nontrivial bounds for their Hausdorff dimension even in the n-dimensional case.

Leadership through the Gender Lens: Women and Men in Organisations

Leadership and management remain highly gendered. Recent decades have seen a major international growth of studies on gender relations in leadership, organisations and management, in both empirical research and theoretical analysis. The differential relations of women and men to leadership and management are a key question for both theory and practice. Recent research and discussion on the gendering of leadership have been influenced by and have addressed: feminism; recognition of women and women’s situations, experiences and voices in leadership; organisational culture; communication; divisions of labour, hierarchy, power and authority; imagery and symbolism; information technology; sexuality, harassment, bullying and violence in organisations; home-work relations; men and masculinities in leadership; globalisation, transnationalism, intersectionality and post¬¬colonialism – amongst other issues. Having said that, the vast majority of mainstream work on leadership retains little or no gender analysis. In most business schools and other universities the position of gender-explicit work on leadership is still not well established. Leadership through the Gender Lens brings together critical analyses and debates on gender, leadership and management with contributions from 13 countries and five continents. How leadership and management are gendered can mean more gender equal or more gender unequal conditions for women and men. This includes how education and training can contribute to gendered leadership and management. The volume is organised in three main sections, on: careers and leadership; management, hierarchy and leadership: and interventions in leadership.