• Publications
  • Influence
L-optimal transportation for ricci flow ∗
We introduce the notion of L-optimal transportation, and use it to construct a natural monotonic quantity for Ricci flow which includes a selection of other monotonicity results, including some keyExpand
  • 39
  • 14
  • PDF
The harmonic map heat flow from surfaces
We present a study of the harmonic map heat flow of Eells and Sampson in the case that the domain manifold is a surface. Particular emphasis has been placed on the singularities which may occur, asExpand
  • 21
  • 8
  • PDF
Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities
We extend the notion of what it means for a complete Ricci flow to have a given initial metric, and consider the resulting well-posedness issues that arise in the 2D case. On one hand we constructExpand
  • 29
  • 6
  • PDF
Local monotonicity and mean value formulas for evolving Riemannian manifolds
Abstract We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first authorExpand
  • 30
  • 6
  • PDF
Decay estimates for Rivière’s equation, with applications to regularity and compactness
We derive a selection of energy estimates for a generalisation of a critical equation on the unit disc in ℝ2 introduced by Riviere. Applications include sharp regularity results and compactnessExpand
  • 32
  • 4
  • PDF
An Example of a Nontrivial Bubble Tree in the Harmonic Map Heat Flow ∗
We present the first example of the formation of a nontrivial bubble tree in the harmonic map heat flow. In other words, we give a flow in which more than one bubble develops at the same point. TheExpand
  • 8
  • 1
  • PDF
Landscape Narratives: the South East Cheviots Project
‘The huts are now roofless, the fires of the hearths quenched for ever, the fortifications levelled; yet these ruins have out-lasted the erections of more civilized times, and they still remain toExpand
  • 6
  • 1
Early Cultivation in Northumberland and The Borders.
Recent discoveries on both sides of the Anglo-Scottish Border have shown that it is now possible to identify the surface remains of prehistoric cultivation without recourse to excavation. NumerousExpand
  • 32
  • 1
Analytical Surveys of Stonehenge and its Environs, 2009–2013: Part 2 – the Stones
Non-invasive survey in the Stonehenge ‘Triangle’, Amesbury, Wiltshire, has highlighted a number of features that have a significant bearing on the interpretation of the site. Geophysical anomaliesExpand
  • 7
  • 1
...
1
2
3
4
5
...