914 reputation
311
bio website scholar.google.com/…
location Jyväskylä
age 28
visits member for 2 years, 7 months
seen yesterday

I am a post-doctoral researcher at University of Jyväskylä. My research interest is geometric function theory, analysis on metric spaces, inverse problems in the plane and metric geometry.


Apr
10
revised Are there any known ``topological" invariants for branched coverings?
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Apr
10
comment Are there any known ``topological" invariants for branched coverings?
@AlexDegtyarev: Take the example as in the homeomorphism case, the linking number of circle and sphere are topological invariant, it can not change from +1 to -1 under a sense-preserving homeomorphism. I want a similar kind of concept, so that they are kept by branched coverings as defined above.
Apr
10
comment Are there any known ``topological" invariants for branched coverings?
@AlexDegtyarev: (1) I noticed that there are different definitions of branched coverings used in different areas. In geometric function theory, one usually defines branched coverings as above and it is not necessarily to be a real covering mapping. (2) I corrected it in 3-dim and in 4 dim, one needs to use circle and sphere. (3). I want some concept defined topologically on $\Omega$ and it still makes senses in the target under the branched covering $f$ so that this concept are kept.
Apr
10
revised Are there any known ``topological" invariants for branched coverings?
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Apr
10
asked Are there any known ``topological" invariants for branched coverings?
Apr
10
revised A lower-dimensional algebraic topology problem between homology group and fundamental group
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Apr
8
comment Should one post a paper on the arXiv if it is not intended to be published?
I think another good way is to establish a personal homepage and then put it up there as a small notes indicating what it is about. At least, many well-known experts in my field did it in this way.
Mar
27
comment A lower-dimensional algebraic topology problem between homology group and fundamental group
@GabrielC.Drummond-Cole: could you please give me one such example? I tried, but still fails, the main problem for me is that I cannot make $\Omega$ a topological ball. Thanks.
Mar
17
comment $H=W$ for weighted Sobolev spaces
@FanZheng As far as I know, the question is very hard. Even in the case $m=1$ and $\mu_0=\mu_1$, the essential known condition for the coincidence are the so-called $p$-admissible weight, where a kind of reverse H\"older's inequality is the key.
Mar
3
comment Publication in proceedings
As far as I know, in mathematics, usually proceeding of a conference gives very high priority to the invited speakers and it is difficult to contribute in a proceeding. Many proceedingsar in celebration/memory of some well-known mathematicians or some bigger conferences will appear in MatheScinet as well.
Mar
3
comment A lower-dimensional algebraic topology problem between homology group and fundamental group
@AlexDegtyarev: Thanks for reminder. Here $C\geq 1$ is an absolute constant. The interesting case is actually $C>1$.
Mar
3
revised A lower-dimensional algebraic topology problem between homology group and fundamental group
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Mar
3
comment A lower-dimensional algebraic topology problem between homology group and fundamental group
@GabrielC.Drummond-Cole: I agree that there is no reason why the implication should hold, but for $n=3$, it seems that it is not easy to use the "wild" examples from topology to serve as a counter-example and so I would like to know whether this is some point hidden for this.
Mar
3
asked A lower-dimensional algebraic topology problem between homology group and fundamental group
Mar
2
comment How to define the determinant of a morphism between graded Lie algebras?
@YCor:In particular, such a Lie algebra admit a group operation * by the BCH formula so that g, with *, becomes a Carnot group of homogenuous dimension $Q=\sum_{i=1}^s i\dim V_i$.
Mar
2
comment How to define the determinant of a morphism between graded Lie algebras?
@YCor: I am sorry that I do not know there are many different notions of this concept. I followed the lecture notes by Enrico, which can be found here sites.google.com/site/enricoledonne/lecture_notes, the stratification of step $s$ means that $g=V_1\oplus V_2\cdots\oplus V_s$, with $[V_j,V_1]=V_{j+1}$ for $1\leq j\leq s-1$ and $V_s\neq \{0\}$.
Mar
2
asked How to define the determinant of a morphism between graded Lie algebras?
Feb
26
comment Coarea formula in a subelliptic context
Pansu's notes is too sketch and no details are given. But of course, he always has the correct intuition.
Feb
22
comment Are there only countably many compact topological manifolds?
If one assumes some quantitative topology, then one indeed also gets quantitative bounds on the number of homotopy type or homeomorphism type. This is the geometric finiteness theorem obtained by Grove-Peterson-Wu 1990.
Feb
14
comment How to decide whether the journal is pure or applied?
Just a short comment: there is this Science Citation Report, published every year. One can find the impact factor and article influence score etc. Usually, if the journal accepts low number of papers and has high article influence score, then it has good reputation.