Related Experiment Video
Updated: Dec 16, 2025
16:01
An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
Published on: September 24, 2017
10.8K
Ultradifferentiable CR Manifolds
1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
Journal of Geometric Analysis
|July 7, 2020
Summary
This study introduces ultradifferentiable CR manifolds and proves regularity for CR mappings using Denjoy-Carleman classes. It also investigates the regularity of infinitesimal CR automorphisms on these manifolds.
Area of Science:
- Differential Geometry
- Complex Analysis
- Harmonic Analysis
Background:
- The study of CR manifolds is a significant area in differential geometry.
- Understanding regularity properties of mappings between manifolds is crucial for geometric analysis.
- Denjoy-Carleman classes provide a framework for analyzing ultradifferentiable functions.
Purpose of the Study:
- To introduce the concept of ultradifferentiable CR manifolds.
- To establish an ultradifferentiable regularity result for finitely nondegenerate CR mappings.
- To investigate the regularity of infinitesimal CR automorphisms on ultradifferentiable abstract CR manifolds.
Main Methods:
- Introduction of ultradifferentiable CR manifolds based on Denjoy-Carleman classes.
- Proof of an ultradifferentiable regularity result for CR mappings.
- Analysis of the regularity of infinitesimal CR automorphisms.
Main Results:
- The notion of ultradifferentiable CR manifold is formally introduced.
- An ultradifferentiable regularity result for finitely nondegenerate CR mappings is established.
- The regularity of infinitesimal CR automorphisms on these manifolds is investigated.
Conclusions:
- The study extends the understanding of regularity in the context of CR manifolds.
- The findings contribute to the theory of ultradifferentiable functions and geometric analysis.
- This work opens avenues for further research into the properties of CR manifolds and their associated mappings.
Keywords:
CR mappingsInfinitesimal CR automorphismsUltradifferentiable CR manifoldsUltradifferentiable regularityMore Related Videos
Related Concept Videos
01:28Forced Transdifferentiation
2.2K
Transdifferentiation, also known as lineage reprogramming, was first discovered by Selman and Kafatos in 1974 in silkmoths. They observed that the moths’ cuticle-producing cells transformed into salt-producing cells. Many such cases of natural transdifferentiation occur in organisms. In humans, pancreatic alpha cells can become beta cells. In newts, the loss of the eye’s lens causes the pigmented epithelial cells to transdifferentiate into the lens cells.
Artificial...
Artificial...
2.2K
01:16Second Uniqueness Theorem
2.6K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
2.6K
01:27Curvilinear Motion: Normal and Tangential Components
708
When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
708
01:15Routh-Hurwitz Criterion I
459
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
459
01:19Degree of Curvature and Radius of Curvature
389
The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of...
389
01:22Second Derivatives and Laplace Operator
2.5K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
2.5K