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Publications Influence

L-optimal transportation for ricci flow ∗

- P. Topping
- 2007

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 key… Expand

39 14- PDF

The harmonic map heat flow from surfaces

- P. Topping
- Mathematics
- 1 April 1996

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, as… Expand

21 8- PDF

Uniqueness and nonuniqueness for Ricci flow on surfaces: Reverse cusp singularities

- P. Topping
- Mathematics
- 14 October 2010

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 construct… Expand

29 6- PDF

Local monotonicity and mean value formulas for evolving Riemannian manifolds

- K. Ecker, Dan Knopf, Lei Ni, P. Topping
- Mathematics
- 18 August 2006

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 author… Expand

30 6- PDF

Decay estimates for Rivière’s equation, with applications to regularity and compactness

- B. Sharp, P. Topping
- Mathematics
- 3 February 2011

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 compactness… Expand

32 4- PDF

Structure and ritual in the Neolithic house:: Some examples from Britain and Ireland

- P. Topping
- Geography
- 1 December 2002

15 4

An Example of a Nontrivial Bubble Tree in the Harmonic Map Heat Flow ∗

- P. Topping
- 2000

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. The… Expand

8 1- PDF

Landscape Narratives: the South East Cheviots Project

- P. Topping, Keith Blood, +8 authors H. Welfare
- Art
- Proceedings of the Prehistoric Society
- 2008

‘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 to… Expand

6 1

Early Cultivation in Northumberland and The Borders.

- P. Topping, S. Halliday, A. Welfare
- Geography
- 1989

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. Numerous… Expand

32 1

Analytical Surveys of Stonehenge and its Environs, 2009–2013: Part 2 – the Stones

- D. Field, H. Anderson-Whymark, +15 authors H. Winton
- Geography
- Proceedings of the Prehistoric Society
- 23 March 2015

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 anomalies… Expand

7 1

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