scholarly journals Hyperbolic Unfoldings of Minimal Hypersurfaces

2018 ◽  
Vol 6 (1) ◽  
pp. 96-128 ◽  
Author(s):  
Joachim Lohkamp
Keyword(s):  
Point Of View ◽  
Hyperbolic Spaces ◽  
Intrinsic Geometry ◽  
Minimal Hypersurfaces ◽  
Bounded Geometry ◽  
New Concepts ◽  
Gromov Hyperbolic ◽  
Area Minimizing ◽  
Conformal Deformations ◽  
Gromov Boundary

Abstract We study the intrinsic geometry of area minimizing hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. Namely, for any such hypersurface H we define and construct a so-called S-structure. This new and natural concept reveals some unexpected geometric and analytic properties of H and its singularity set Ʃ. Moreover, it can be used to prove the existence of hyperbolic unfoldings of H\Ʃ. These are canonical conformal deformations of H\Ʃ into complete Gromov hyperbolic spaces of bounded geometry with Gromov boundary homeomorphic to Ʃ. These new concepts and results naturally extend to the larger class of almost minimizers.

scholarly journals Spirals of Sustainable Academic Motivation, Creativity, and Trust of Higher Education Staff

2021 ◽  
Vol 13 (13) ◽  
pp. 7057
Author(s):  
Martina Blašková ◽  
Dominika Tumová ◽  
Rudolf Blaško ◽  
Justyna Majchrzak-Lepczyk
Keyword(s):  
Higher Education ◽  
Academic Motivation ◽  
Slovak Republic ◽  
Point Of View ◽  
Scientific Management ◽  
Administrative Staff ◽  
Sustainable Systems ◽  
New Concepts ◽  
Future Improvement ◽  
The University

Sustainability has to penetrate more and more into higher education. It should not focus only on traditional elements. It should also enter new, but for future improvement, extremely important areas. Based on this premise, creativity and motivation, when additionally interconnected and supported by trust that is provided and achieved, decide on the progress and sustainability of universities. This connection is gaining importance especially from the point of view of building solid foundations and mechanisms that functionally preserve the potential effects of these elements in the future. For this reason and following the nature, importance, and content of sustainable academic motivation (SAM), the paper introduces two new concepts: sustainable academic creativity (SAC) and sustainable academic trust (SAT). For further original contributions, the paper hypothesizes the existence of mutual—spiral—relations of sustainable academic motivation (SAM), sustainable academic creativity (SAC), and sustainable academic trust (SAT). The empirical section tests the validity of this claim in the universities of two countries: the Slovak Republic and Poland. A survey performed on a sample of n=181 pedagogical, scientific, management, and administrative staff in higher education confirms the existence of these spirals. The results indicate the spiral effect of motivation when connected with creativity and trust and show that it is accented by the crucial principles of sustainability (responsibility, novelty, usefulness, progress, etc.). Therefore, the paper’s conclusion contains the explanations for the potential occurrence of three types of sustainably mutual systems and complexes. These are: (a) individual sustainable systems of SAM, SAC, and SAT; (b) group/sectional sustainable systems of SAM, SAC, and SAT; and (c) the global sustainable complex of SAM, SAC, and SAT in the university.

scholarly journals Coarse median algebras: the intrinsic geometry of coarse median spaces and their intervals

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Graham A. Niblo ◽  
Nick Wright ◽  
Jiawen Zhang
Keyword(s):  
Finite Rank ◽  
Intrinsic Geometry ◽  
Bounded Geometry ◽  
Higher Dimensional ◽  
Median Algebra ◽  
Asymptotic Geometry ◽  
Median Operator

AbstractThis paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov’s concept of $$\delta $$ δ -hyperbolicity.

Bounded properties of curvatures of perturbed Ricci metric on curve moduli

2014 ◽  
Vol 25 (12) ◽  
pp. 1450113
Author(s):  
Xiaorui Zhu
Keyword(s):  
Finite Volume ◽  
Ricci Curvature ◽  
Moduli Space ◽  
Point Of View ◽  
Bisectional Curvature ◽  
Bounded Geometry ◽  
Holomorphic Bisectional Curvature ◽  
Chern Form ◽  
Thick Part ◽  
Kahler Metric

As is well-known, the Weil–Petersson metric ωWP on the moduli space ℳg has negative Ricci curvature. Hence, its negative first Chern form defines the so-called Ricci metric ωτ. Their combination [Formula: see text], C > 0, introduced by Liu–Sun–Yau, is called the perturbed Ricci metric. It is a complete Kähler metric with finite volume. Furthermore, it has bounded geometry. In this paper, we investigate the finiteness of this new metric from another point of view. More precisely, we will prove in the thick part of ℳg, the holomorphic bisectional curvature of [Formula: see text] is bounded by a constant depending only on the thick constant and C0 when C ≥ (3g - 3)C0, but not on the genus g.

scholarly journals FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES

2004 ◽  
Vol 14 (02) ◽  
pp. 115-171 ◽  
Author(s):  
ILYA KAPOVICH ◽  
RICHARD WEIDMANN
Keyword(s):  
Hyperbolic Group ◽  
Conjugacy Classes ◽  
Hyperbolic Spaces ◽  
Gromov Hyperbolic ◽  
Torsion Free

We obtain a number of finiteness results for groups acting on Gromov-hyperbolic spaces. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of n-generated one-ended subgroups.

scholarly journals Environmental Hydraulics Research

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2749
Author(s):  
Helena M. Ramos ◽  
Armando Carravetta ◽  
Aonghus Mc Nabola ◽  
Kemi Adeyeye
Keyword(s):  
Field Experiments ◽  
Water Environment ◽  
Point Of View ◽  
Physical Models ◽  
Advanced Materials ◽  
Environmental Hydraulics ◽  
New Concepts ◽  
Disciplinary Field ◽  
To Come ◽  
Available Information

Environmental hydraulics research includes the different domains of hydrodynamics, such as the investigation and implementation of the physical and experimental applications, and research into the quantity, quality, modelling and simulation of the attributes associated with flowing water. This topic is studied both from a technical and environmental point of view, with the objective of protecting and enhancing the quality of the environment. It is a cross-disciplinary field of study which comprises open channel/river flows and pressurised systems, combining, among others, new technological, social, and environmental hydraulic challenges. It provides researchers and engineers working in water-related fields with available information, new concepts and tools, new design solutions, eco-friendly technologies, and the advanced materials necessary to address the increasing challenges of ensuring a sustainable water environment—that is, a water environment effectively managed and adequated for generations to come by promoting the adaptation, flexibility, integration and sustainability of recognised environmental solutions. Using advanced numerical and physical models in field experiments, and tests in different types of laboratory set-ups, specialists in environmental hydraulics produce the best analyses, concepts, techniques, tools, and solutions to environmental hydraulic problems, as well as in relation to the water, energy and environmental nexus.

Experimental Programs: SMSG—one point of view

1962 ◽  
Vol 55 (6) ◽  
pp. 476-478
Author(s):  
Lillian Marlin
Keyword(s):  
Approaches To Learning ◽  
Point Of View ◽  
School Mathematics ◽  
Modern World ◽  
Study Group ◽  
Prime Mover ◽  
High School Mathematics ◽  
New Concepts ◽  
New Material ◽  
And Mathematics

The modern world, with its emphasis on science and mathematics, has given birth to new concepts in these fields. The dire need for trained mathematicians and an informed public resulted in the recognition of the need to incorporate into the study of mathematics new material and to present the old in a new light. The School Mathematics Study Group material is a prime mover in this field; it offers the new topics and language of elementary and high school mathematics, using modern approaches to learning.

CLOSED MINIMAL HYPERSURFACES IN COMPACT SYMMETRIC SPACES

1992 ◽  
Vol 03 (05) ◽  
pp. 629-651 ◽  
Author(s):  
CLAUDIO GORODSKI
Keyword(s):  
Symmetric Spaces ◽  
Local Geometry ◽  
Minimal Hypersurfaces ◽  
Compact Symmetric Space ◽  
Orbital Geometry ◽  
Rank One ◽  
Minimal Cones ◽  
Area Minimizing ◽  
Simply Connected ◽  
Minimal Embedding

W.Y. Hsiang, W.T. Hsiang and P. Tomter conjectured that every simply-connected, compact symmetric space of dimension ≥4 must contain some minimal hypersurfaces of sphere type. With the aid of equivariant differential geometry, they showed that this is in fact the case for many symmetric spaces of rank one and two. Let M be one of the symmetric spaces: Sn(1)×Sn(1)(n≥4), SU(6)/Sp(3), E6/F4, ℍP2 (quaternionic proj. plane) or CaP2 (Cayley proj. plane). We prove the existence of infmitely many immersed, minimal hypersurfaces of sphere type in M which are invariant under a certain group G of isometries of M. Following Hsiang and the others, the equivariant method is also used here to reduce the problem to an investigation of geodesics in M/G equipped with a metric (with singularities) depending only on the orbital geometry of the transformation group (G, M). However, our constructions are based on area minimizing homogeneous cones, corresponding to a corner singularity of M/G with the local geometry of nodal type; this can be viewed as a variation of some of their constructions which depended on some unstable minimal cones of focal type. We further apply the equivariant method to construct a minimal embedding of S1×Sn−1×Sn−1 into Sn(1)×Sn(1)(n≥2) and a minimal, embedded hypersurface of sphere type in [Formula: see text], ℍPn×ℍPn (n≥2) and CaP2×CaP2.

Sixteenth Canadian Geotechnical Colloquium: Frost heave in soils: concepts and engineering

1994 ◽  
Vol 31 (2) ◽  
pp. 223-245 ◽  
Author(s):  
J.-M. Konrad
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Point Of View ◽  
Frost Heave ◽  
Fundamental Point ◽  
New Concepts ◽  
Segregation Potential ◽  
Thermal Histories ◽  
Ice Content ◽  
Lens Formation

Frost heave in soils is analysed from a fundamental point of view to predict the development of periodic ice lens formation that is observed in frozen soils. A model of simultaneous heat and mass transfer associated with three new concepts is described and was found to exhibit many of the frost heave features observed in laboratory tests. An efficient frost heave parameter termed the segregation potential, SP, is also described and found to be an adequate input to a general formulation of heat and mass transfer for the prediction of frost heave in soils for both laboratory and field conditions. Representative values of SP depend on the stress and thermal histories of the soil deposit. The SP-based approach can be used for solving two-dimensional frost heave problems and yields stress, temperature, and ice-content distributions with time. Key words : frost heave, soils, segregation potential, simulation, thermodynamics.

scholarly journals Perceptions of Prospective ICT Teachers Regarding Usability of Subliminal Message Techniques in Education

2017 ◽  
Vol 13 (7) ◽  
pp. 81
Author(s):  
Hasan Arslan ◽  
Muzaffer Ozdemir ◽  
Meltem Kuscu
Keyword(s):  
Qualitative Research ◽  
Information Technologies ◽  
Point Of View ◽  
Instructional Technologies ◽  
Human Behaviors ◽  
Senior Class ◽  
Interview Technique ◽  
New Concepts ◽  
Subliminal Messages ◽  
The Brain

Human brain is two hemispheres filled with secrets. What happens in the brain has always a research source and mystery for human. Some researchers associating human behaviors with the subconscious reported that if they reached to subconscious they could make the human demonstrate the desired behaviors. Researchers thinking like that have become the essential advisors for the advertisement sector trying to direct people to consumption especially. While the advertisement sector tries to make people buy things that dont need it also brought new concepts in the science world. The most known and emphasized one are subliminal messages. The purpose of this study is to examine use of subliminal messages for education from the point of view of students Computer and Instructional Technologies Education (CEIT). Since subliminal messages are dealt in terms of information technologies generally, opinions of CEIT senior class students dominating this field were referred. Interview technique one of the qualitative research methods was used in the study. In this study 42 students participated in the research. According to findings of the study, CEIT students expressed an opinion that subliminal messages could be beneficial for the education. It was found out that the most preferred method for education materials to be prepared is cartoon for students. It was expressed that 25. square technique was the most proper method as the subliminal method.

scholarly journals Rough isometry between Gromov hyperbolic spaces and uniformization

2021 ◽  
Vol 46 (1) ◽  
pp. 449-464
Author(s):  
Jeff Lindquist ◽  
Nageswari Shanmugalingam
Keyword(s):  
Hyperbolic Spaces ◽  
Gromov Hyperbolic ◽  
Rough Isometry
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