390 reputation
18
bio website
location Jyväskylä
age 27
visits member for 1 year, 7 months
seen 10 hours ago

I am a post-doctoral researcher at University of Jyväskylä. My research interest is geometric function theory and analysis on metric spaces.


Mar
25
answered Jacobian of an injective mapping
Mar
24
revised How many ways do we have to prove that a mapping is open?
added 397 characters in body
Mar
11
comment Is the multiplicity of a Sobolev mapping alwasys locally essentially bounded?
To Fernando Muro:Ifeel like one needs some topological assumption for $f$ to ensure that one can prove such a result. On the other hand, to prove such a result, one needs to use degree theory or other more algebraic topological concept. That is why I add this label.
Mar
11
asked Is the multiplicity of a Sobolev mapping alwasys locally essentially bounded?
Mar
6
comment How many ways do we have to prove that a mapping is open?
To ACL: the result you mentioned is the invariance of the domain, which is a simply application of degree theory. Here I am looking for more analytic assumptions on $f$, instead of strong topological assumptions, like you mentioned local injectivity.
Mar
6
revised How many ways do we have to prove that a mapping is open?
added 10 characters in body
Feb
28
answered Quasiconformal extensions of diffeomorphisms
Feb
28
accepted Is there a direct proof of the following real analysis fact?
Feb
28
revised Is there a direct proof of the following real analysis fact?
added 1 characters in body
Feb
28
asked Is there a direct proof of the following real analysis fact?
Jan
5
comment quasiconformal across the real line
As I mentioned above, the reason for $f(x)=xsin(1/x)$ (when defined to be 0 at 0 to make it continuous) fails to be AC is that $f$ is not a function of bounded variation since it oscilate too much around the point zero.
Jan
5
answered quasiconformal across the real line
Dec
23
awarded  Critic
Dec
22
comment Does anyone know what is the right reference for the following simple lemma from harmonic analysis?
To Benjamin Dickman: thank you very much and I will check that paper.
Dec
21
comment A problem related to connectivity of analytic functions
Could you please remind me how does one prove $f(\mathbb{D})$ is 1 when $f(z)$ is proper?
Dec
21
comment Sobolev spaces on boundaries
My comment is addressing the his second definition of Sobolev spaces. If one imposes smooth condition on M, then one can naturally define the Sobolev spaces via local coordinate. In this manner, the foudamental theorem of calculus is implicitely used. In the non-smooth case (on metric measure spaces), one can define the Sobolev spaces in a similar manner. This is certainly non-trivial and relies on the recent development on non-smooth calculus.
Dec
21
comment Does anyone know what is the right reference for the following simple lemma from harmonic analysis?
To Alexandre Eremenko: Yes. We know the unpublished note is earier than the cited reference by Bojarski. But we do not know whether actually someone proves this fact even earlier. I think the name should give to the first person who has proved this.
Dec
21
asked Does anyone know what is the right reference for the following simple lemma from harmonic analysis?
Dec
21
answered Sobolev spaces on boundaries
Dec
17
comment Lipschitz boundary vs rectifiable curve boundary
I do not quit understand your question. What happens just take a domain D in the plane with a single cusp? The boundary of D is a rectifiable Jordan curve, but it is not Lipshichtz.