Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Tuomas Orponen"'
Autor:
Katrin Fässler, Tuomas Orponen
Publikováno v:
Bulletin of the London Mathematical Society.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1ae2fd28b8cbb74706f4d3be2da409c7
https://doi.org/10.1112/blms.12844
https://doi.org/10.1112/blms.12844
Autor:
Hannu Tuomas Orponen
Publikováno v:
Geometric and Functional Analysis. 32:81-134
Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: \alpha$ and $\dim_{\mathrm{H}} B =: \beta$. I prove that $$\dim_{\mathrm{H}} [A + \theta B] \geq \alpha + \beta \cdot \tfrac{1 - \alpha}{2 - \alpha}$$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40d5fb9e7187d308baae52b129402288
https://doi.org/10.1007/s00039-021-00589-x
https://doi.org/10.1007/s00039-021-00589-x
Autor:
Tuomas Orponen, Katrin Fässler
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 153:30-113
Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \ma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ece22bd616da991ee52d025d02ecb20d
https://doi.org/10.1016/j.matpur.2021.07.004
https://doi.org/10.1016/j.matpur.2021.07.004
Publikováno v:
International Mathematics Research Notices. 2022:17909-17975
Two definitions for the rectifiability of hypersurfaces in Heisenberg groups $\mathbb{H}^n$ have been proposed: one based on ${\mathbb{H}}$-regular surfaces and the other on Lipschitz images of subsets of codimension-$1$ vertical subgroups. The equiv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b45b7d6cf665d3cc38bf26ef43486f78
https://doi.org/10.1093/imrn/rnab227
https://doi.org/10.1093/imrn/rnab227
Autor:
Tuomas Orponen
Publikováno v:
Inventiones mathematicae. 226:653-709
I prove that a closed $n$-regular set $E \subset \mathbb{R}^{d}$ with plenty of big projections has big pieces of Lipschitz graphs. This answers a question of David and Semmes.
Comment: 40 pages. v3: referee comments incorporated
Comment: 40 pages. v3: referee comments incorporated
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::de35925f85cf3016df434218bcb98454
https://doi.org/10.1007/s00222-021-01055-z
https://doi.org/10.1007/s00222-021-01055-z
Publikováno v:
International Mathematics Research Notices.
We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is a compact set that contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45a9ac2aad7d294b8361a0383de4f1e4
https://doi.org/10.1093/imrn/rnac168
https://doi.org/10.1093/imrn/rnac168
Autor:
Tuomas Orponen, Michele Villa
Publikováno v:
Advances in Calculus of Variations.
A flag domain in $\mathbb{R}^{3}$ is a subset of $\mathbb{R}^{3}$ of the form $\{(x,y,t) : y < A(x)\}$, where $A \colon \mathbb{R} \to \mathbb{R}$ is a Lipschitz function. We solve the Dirichlet and Neumann problems for the sub-elliptic Kohn-Laplacia
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf7357cdc2c37bc62202a0f391ad51ca
https://doi.org/10.1515/acv-2021-0077
https://doi.org/10.1515/acv-2021-0077
Publikováno v:
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society, American Mathematical Society, 2020, 373 (8), pp.5957-5996. ⟨10.1090/tran/8146⟩
Transactions of the American Mathematical Society, American Mathematical Society, 2020, 373 (8), pp.5957-5996. ⟨10.1090/tran/8146⟩
A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8dc5594f61e50297d2f6b294ced7b3e7
https://doi.org/10.1090/tran/8146
https://doi.org/10.1090/tran/8146
Autor:
Katrin Fässler, Tuomas Orponen
Publikováno v:
Bulletin of the London Mathematical Society. 52:472-488
A theorem of Dorronsoro from the 1980s quantifies the fact that real-valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5dd8ee547064e5c17276e3d9da91d632
https://doi.org/10.1112/blms.12341
https://doi.org/10.1112/blms.12341
Let $\mathcal{G}(d,n)$ be the Grassmannian manifold of $n$-dimensional subspaces of $\mathbb{R}^{d}$, and let $\pi_{V} \colon \mathbb{R}^{d} \to V$ be the orthogonal projection. We prove that if $\mu$ is a compactly supported Radon measure on $\mathb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5b5318113016e145ba4371ea63ed757
http://urn.fi/urn:nbn:fi-fe2022112967578
http://urn.fi/urn:nbn:fi-fe2022112967578
