Polyhedral approximation and uniformization for non-length surfaces

D Ntalampekos, M Romney - Journal of the European Mathematical …, 2024 - ems.press
We prove that any metric surface (that is, metric space homeomorphic to a 2-manifold with
boundary) with locally finite Hausdorff 2-measure is the Gromov–Hausdorff limit of …

Quasiconformal almost parametrizations of metric surfaces

D Meier, S Wenger - Journal of the European Mathematical Society, 2024 - ems.press
We look for minimal conditions on a two-dimensional metric surface X of locally finite
Hausdorff 2-measure under which X admits an (almost) parametrization with good geometric …

Uniformization of metric surfaces using isothermal coordinates

T Ikonen - arXiv preprint arXiv:1909.09113, 2019 - arxiv.org
We establish a uniformization result for metric surfaces-metric spaces that are topological
surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of …

Coarea inequality for monotone functions on metric surfaces

B Esmayli, T Ikonen, K Rajala - Transactions of the American Mathematical …, 2023 - ams.org
We study coarea inequalities for metric surfaces—metric spaces that are topological
surfaces, without boundary, and which have locally finite Hausdorff 2-measure $\mathcal …

Maximal metric surfaces and the Sobolev-to-Lipschitz property

P Creutz, E Soultanis - Calculus of Variations and Partial Differential …, 2020 - Springer
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors
regular spheres these are uniquely characterized by satisfying the seemingly unrelated …

On conformal planes of finite area

A Lytchak - Mathematische Zeitschrift, 2023 - Springer
On conformal planes of finite area | Mathematische Zeitschrift Skip to main content
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Mathematische …

Geometric analogy between quantum dynamics and curved space through quantum hydrodynamics

T Shushi - Classical and Quantum Gravity, 2023 - iopscience.iop.org
In general relativity, the dynamics of objects is governed by the curvature of spacetime,
which is caused by the presence of matter and energy. In contrast, in quantum mechanics …

The branch set of minimal disks in metric spaces

P Creutz, M Romney - International Mathematics Research …, 2023 - academic.oup.com
We study the structure of the branch set of solutions to Plateau's problem in metric spaces
satisfying a quadratic isoperimetric inequality. In our 1st result, we give examples of spaces …

Definitions of quasiconformality on metric surfaces

D Meier, K Rajala - arXiv preprint arXiv:2405.07476, 2024 - arxiv.org
We explore the interplay between different definitions of distortion for mappings $ f\colon
X\to\mathbb {R}^ 2$, where $ X $ is any metric surface, meaning that $ X $ is homeomorphic …

Disk patterns, quasi-duality and the uniform bounded diameter conjecture

Y Luo, Y Zhang - arXiv preprint arXiv:2408.10344, 2024 - arxiv.org
We show that the diameter of the image of the skinning map on the deformation space of an
acylindrical reflection group is bounded by a constant depending only on the topological …