A5065009980- Geometric Analysis and Curvature Flows
- Nonlinear Partial Differential Equations
- Advanced Topology and Set Theory
- Analytic and geometric function theory
- Mathematical Dynamics and Fractals
- Advanced Banach Space Theory
- Advanced Differential Geometry Research
- Point processes and geometric inequalities
- Advanced Mathematical Modeling in Engineering
- Numerical methods in inverse problems
- Geometry and complex manifolds
- advanced mathematical theories
- Mathematical and Theoretical Analysis
- Dermatological and Skeletal Disorders
- Functional Equations Stability Results
- Holomorphic and Operator Theory
- Geometric and Algebraic Topology
- Homotopy and Cohomology in Algebraic Topology
- Advanced Numerical Analysis Techniques
- Rings, Modules, and Algebras
- Advanced Harmonic Analysis Research
- Topological and Geometric Data Analysis
- Fuzzy and Soft Set Theory
- Approximation Theory and Sequence Spaces
- Optimization and Variational Analysis
University of Bern
2014-2025
Friedrich-Alexander-Universität Erlangen-Nürnberg
2022-2023
Aalto University
2022-2023
Walter de Gruyter (Germany)
2022-2023
Semmelweis University
2021
University of Illinois Urbana-Champaign
2017
Montana State University
2017
ETH Zurich
2016
Université Paris-Sud
2016
University of Crete
2013
We give an estimate for the distance function related to Kobayashi metric on a bounded strictly pseudoconvex domain with C 2 -smooth boundary.Our formula relates Carnot-Carathéodory boundary.The is precise up additive term.As corollary we conclude that equipped this hyperbolic in sense of Gromov.
We establish geometric inequalities in the sub-Riemannian setting of Heisenberg group $$\mathbb H^n$$ . Our results include a natural version celebrated curvature-dimension condition Lott–Villani and Sturm also geodesic Borell–Brascamp–Lieb inequality akin to one obtained by Cordero-Erausquin, McCann Schmuckenschläger. The latter statement implies versions Prékopa–Leindler Brunn–Minkowski inequalities. proofs are based on optimal mass transportation Riemannian approximation developed...
In this paper, we study isometries of $p$-Wasserstein spaces. our first result, for every complete and separable metric space $X$ $p\geq1$, construct a $Y$ such that embeds isometrically into $Y$, the over admits mass-splitting isometries. Our second result is about embeddings rigid constructions. We show any can be embedded $1$-Wasserstein rigid.
We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.
We compare the Hausdorff measures and dimensions with respect to Euclidean Heisenberg metrics on first group.The result is a dimension jump described by two inequalities.The sharpness of our estimates shown examples.Moreover comparison between H-rectifiability given.
We consider horizontal iterated function systems in the Heisenberg group that are contrast with non-existence of Lipschitz surfaces which was recently proved by Ambrosio and Kirchheim (Rectifiable sets metric Banach spaces. Math. Ann.318(3) (2000), 527–555).
We propose a method by modulus of curve families to identify extremal quasiconformal mappings in the Heisenberg group.This approach allows study minimizers not only for maximal distortion but also mean functional, where candidate map is required have constant distortion.As counterpart classical Euclidean problem, we consider class between two spherical annuli group.Using logarithmic-type coordinates can define an analog radial stretch and discuss its properties both with respect...