Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 203 / 1 / d

Table of contents
- Solution d

Solution

The parameterization in part (c) gives the exact self-similarity

K_{λ^{2} t} = λ K_{t}

for every

λ > 0

. The Loewner local growth property supplies a continuous Loewner driving function

U

. Under this scaling of the hulls, the deterministic scaling rule for the Chordal Loewner equation gives

U_{λ^{2} t} = λ U_{t} .

Taking

t = 1

and

λ = t

shows that

U_{t} = U_{1} t = c t

for the real constant

c = U_{1}

.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version