## New answers tagged hausdorff-dimension

8
votes

Accepted

### Maximal Hausdorff dimension of the set on which derivatives do not agree

I think the paper "A singular function with a non-zero finite derivative on a dense set with Hausdorff dimension one"
answers exactly this question.

4
votes

Accepted

### Dimension of the graph of a function $\varphi : \mathbb R^2 \to \mathbb R$

I don't believe it necessary that the dimension of the graph of $\varphi$ be larger than 2. An example is provided by examining Poisson's integral formula for the upper half plane:
$$
u(x,y) = \frac{...

1
vote

### Dimension of the graph of a function $\varphi : \mathbb R^2 \to \mathbb R$

This answer is not complete (I am not sure that the function below is smooth).
It seems $\dim_{\mathbb{H}} G(\varphi)$ may be exactly $2$.
Let $f:\mathbb{R}\to\mathbb{R}$ be any continuous function, ...

Top 50 recent answers are included

#### Related Tags

hausdorff-dimension × 106geometric-measure-theory × 28

fractals × 28

measure-theory × 23

mg.metric-geometry × 19

dimension-theory × 19

hausdorff-measure × 18

reference-request × 13

real-analysis × 10

gn.general-topology × 8

diophantine-approximation × 6

ds.dynamical-systems × 5

ca.classical-analysis-and-odes × 4

harmonic-analysis × 4

fa.functional-analysis × 3

set-theory × 3

cv.complex-variables × 3

fourier-analysis × 3

ergodic-theory × 3

metric-spaces × 3

packing-and-covering × 3

expectation × 3

dg.differential-geometry × 2

gt.geometric-topology × 2

lie-groups × 2