Personal profile

Research interests

The questions I am interested in mix geometry with partial differential equations.

Geometric evolution equations: here we deform geometric objects in a smooth way to help us understand their shape. This is a very powerful recent technique in geometric analysis, and has been crucial in solving many open geometric questions, including the Poincare conjecture (proved by Perelman).

Eigenvalue estimates: Every geometric object has a set of numbers attached to it, called the spectrum. These are like the resonant frequencies of drum. I am interested in how the shape of the object affects the spectrum.

Capillary surfaces and the calculus of variations: Consider a meniscus--- the interface between the water in a glass and the air above it. The special shape of the meniscus is due to an interplay between the energy used in the water/glass interface and the air/water interface, and the gravitational energy--- the shape we see will minimise the sum of these energies. It will also dependent on the shape of the glass and the volume of the water. This is a typical problem in thecalculus of variations, where minimizing a physical quantity can give rise to interesting geometric shapes.

Monash teaching commitment

Second semester 2017:

M41022 Partial Differential Equations

MTH3160 Functional Analysis 

 

 

Keywords

  • eigenvalues
  • parabolic equations
  • heat flow
  • geometric analysis
  • calculus of variations
  • geometric evolution equations
  • mean curvature flow
  • spectral theory

Network Recent external collaboration on country level. Dive into details by clicking on the dots.

Projects 2013 2019

Research Output 1998 2017

Non-concavity of Robin eigenfunctions

Clutterbuck, J. F., Hauer, D. & Andrews, B. 8 Nov 2017 48 p.

Research output: OtherWorking Paper

File

Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue

Andrews, B. & Clutterbuck, J. F. 2013 In : Analysis & PDE. 6, 5, p. 1013 - 1024 12 p.

Research output: Research - peer-reviewArticle

Proof of the fundamental gap conjecture

Andrews, B. & Clutterbuck, J. F. 2011 In : Journal of the American Mathematical Society. 24, 3, p. 899 - 916 18 p.

Research output: Research - peer-reviewArticle

Stability of mean convex cones under mean curvature flow

Clutterbuck, J. F. & Schnurer, O. C. 2011 In : Mathematische Zeitschrift. 267, 3-4, p. 535 - 547 13 p.

Research output: Research - peer-reviewArticle

A capillarity problem for compressible liquids

Athanassenas, M. & Clutterbuck, J. 2009 In : Pacific Journal of Mathematics. 243, 2, p. 213 - 232 20 p.

Research output: Research - peer-reviewArticle

Prizes

Gavin Brown Prize

Julie Faye Clutterbuck (Recipient), 2014

Prize: Prize (including medals and awards)

Activities 2017 2018

  • 3 Contribution to conference
  • 1 External research and teaching

Scientific director, AMSI Winter School

Clutterbuck, J. F. (Chair/ Co-Chair)
2 Jul 201813 Jul 2018

Activity: External research and teaching

New Zealand MathematicalSociety Colloquium

Clutterbuck, J. F. (Keynote/plenary speaker)
5 Dec 20177 Dec 2017

Activity: Contribution to conference

Workshop

Clutterbuck, J. F. (Organiser)
16 Oct 201728 Oct 2017

Activity: Contribution to conference