Projects per year

## 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 the*calculus 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

## Projects 2013 2019

- 1 Active

## Curvature flows and spectral estimates.

Australian Research Council (ARC)

1/07/13 → 31/03/19

Project: Research

## Research Output 1998 2013

## 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-review › Article

## 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-review › Article

## 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-review › Article

## 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-review › Article

## Lipschitz bounds for solutions of quasilinear parabolic equations in one space variable

Andrews, B. & Clutterbuck, J. F. 2009 In : Journal of Differential Equations. 246, 11, p. 4268 - 4283 16 p.Research output: Research - peer-review › Article

## Prizes

## Activities 2017 2018

## Joint PDE and Geometric Analysis Meeting: Australian National University, Pacific Institute of Mathematical Sciences, Beijing International Centre for Mathematical Research

Clutterbuck, J. F. (Organiser)Activity: Contribution to conference

## Scientific director, AMSI Winter School

Clutterbuck, J. F. (Chair/ Co-Chair)Activity: External research and teaching

## New Zealand MathematicalSociety Colloquium

Clutterbuck, J. F. (Keynote/plenary speaker)Activity: Contribution to conference