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A survey of geometric structure in geometric analysis

Shing-Tung Yau
2011 Surveys in Differential Geometry  
In the following lectures, we shall focus on an important branch of geometric analysis: the construction of geometric structures over a given topological space.  ...  The subject of geometric analysis evolves according to our understanding of geometry and analysis.  ...  There is another geometric structure that is of importance in surface theory. This is the line field structure (with singularity) on a surface.  ... 
doi:10.4310/sdg.2011.v16.n1.a7 fatcat:qpxqtosqf5dkviuzvnbjez2zra

Localization of 3D Anatomical Point Landmarks in 3D Tomographic Images Using Deformable Models [chapter]

Sönke Frantz, Karl Rohr, H. Siegfried Stiehl
2000 Lecture Notes in Computer Science  
To model the surface at a landmark, we use quadric surfaces combined with global deformations.  ...  In this paper, we introduce a new approach to 3D landmark localization based on deformable models, which takes into account more global image information in comparison to differential approaches.  ...  Geometric Models of Tips and Saddle Structures As 3D shape prototypes, we here use quadric surfaces, namely, ellipsoids for 3D tip-like structures and hyperboloids of one sheet for 3D saddle structures  ... 
doi:10.1007/978-3-540-40899-4_50 fatcat:mlid67lh2rhlzf3v66skmvsbzy

Impact of roughness of discontinuities on the behaviour of jointed rock samples

Patrycja Jarczyk, E. Pilecka, T. Tatara, J.P. Kogut
2019 E3S Web of Conferences  
Before the three-axial compression tests, the discontinuity surfaces were scanned and parameters describing the geometrical structure of these surfaces were determined.  ...  The subject of the publication is the behavior of rock samples faulted by individual discontinuities with different roughness under three-axial compression conditions, with confining pressures up to 30  ...  The surfaces of these discontinuities had various geometrical structures.  ... 
doi:10.1051/e3sconf/201910601006 fatcat:dru6qjgq6zfbnor53d343mhl5e

Page 2440 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
Then he deals with the problem of determining locally a morphism of geometric structures from some infinitesimal conditions.  ...  The author studies the existence of the geometric substructures of a given geometric structure.  ... 

The Theoretical Study of Kink Deformation in Graphite Based on Differential Geometric Method

Xiao-Wen Lei, Shungo Shimizu, Jin-Xing Shi
2022 Nanomaterials  
micro- and macro-scale material structures with laminated layers.  ...  Kink deformation is often observed in materials with laminated layers. Graphite composed of stacked graphene layers has the unique laminated structure of carbon nanomaterials.  ...  The establishment of a general deformation theory based on a differential geometric method is expected to elucidate the deformation mechanism in laminated structures, e.g., graphite in the present work  ... 
doi:10.3390/nano12060903 pmid:35335716 pmcid:PMC8948689 fatcat:7hmj6eioyjdotc5ocdwfqxctx4

A Damage Identification Method Based on Differential Gradient of Normalized Strain

Ling Ling Lu, Chen Guang Huang, Xi Wang
2013 Applied Mechanics and Materials  
deformation due to geometric inhomogeneity.  ...  In the experiment, differential of strain contour density (DSCD), which has the same physical meaning with DGNS,significantly improves the smoothness and visualization of field information.  ...  The deformation field on the surface of the structure opposite the grooved one is used to detect the damage.  ... 
doi:10.4028/ fatcat:f7ekmokgsrgdda7jhdabftb254

Page 5920 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
This paper studies the following question: Can any complex compact manifold be deformed to a manifold which can be equipped with a real structure or at least to a manifold with an anti-automorphism?  ...  And the latter is the viewpoint of differential geometry, etc., that regards them as problems of intrinsic structure originated by Gauss.  ... 

Hierarchical Shape Matching for Temporally Consistent 3D Video

Chris Budd, Peng Huang, Adrian Hilton
2011 2011 International Conference on 3D Imaging, Modeling, Processing, Visualization and Transmission  
In this paper we present a novel approach for temporal alignment of reconstructed mesh sequences with non-rigid surfaces to obtain a consistent representation.  ...  This gives a tree structure which represents the optimal path for alignment of each frame in the sequence to minimize the change in shape.  ...  Perform the ICP variant on these patches Deform the source mesh with surface Laplacian deformation With each iteration the size of the patches is decreased allowing a coarse-to-fine matching with increasing  ... 
doi:10.1109/3dimpvt.2011.29 dblp:conf/3dim/BuddHH11 fatcat:h2dzg42lzjh6vip23otj2sbfde

Geometric Integrability of Some Generalizations of the Camassa-Holm Equation

Ognyan Christov
2011 International Journal of Differential Equations  
We show that Kupershmidt deformations of these equations describe pseudospherical surfaces and hence are geometrically integrable.  ...  We study the Camassa-Holm (CH) equation and recently introducedμCH equation from the geometric point of view.  ...  DD VU 02/90 with NSF of Bulgaria.  ... 
doi:10.1155/2011/738509 fatcat:mr6jhktvojasngm2t3v7k7jpjy

µ-Holomorphic Projective Connections and Conformal Covariance

Mohamed Kachkachi
2004 Journal of Nonlinear Mathematical Physics  
Here we interpret geometrically this conformal covariance as an exact µholomorphy condition on a two-dimensional Riemann surface Σ on which the model is constructed.  ...  Here we get its transformation law with respect to a quasiconformal transformation on any complex Riemann surface and we recover the transformation law of a holomorphic projective connection under a holomorphic  ...  Then a Riemann surface Σ is a C ∞ -differentiable twodimensional manifold endowed with a reference complex structure (z, z) ( in the sense that (z, z) is associated to the Beltrami differential µ (z, z  ... 
doi:10.2991/jnmp.2004.11.1.2 fatcat:dbbufdaecnaclizy3jgxp2gcme

Computational analysis of lung deformation after murine pneumonectomy

Nenad Filipovic, Barry C. Gibney, Dalibor Nikolic, Moritz A. Konerding, Steven J. Mentzer, Akira Tsuda
2012 Computer Methods in Biomechanics and Biomedical Engineering  
To investigate the hypothesis that parenchymal deformation may trigger lung regeneration, we used microCT scanning to create 3-dimensional finite element geometric models of the murine lung pre-and post-pneumonectomy  ...  Consistent with previously identified growth patterns, subpleural regions of enhanced deformation are compatible with a mechanical signal-likely involving parenchymal stretchtriggering lung growth.  ...  Results The 3D geometric models were constructed with a greater number of surface elements in the post-pneumonectomy object (35,210 elements) than in the pre-pneumonectomy object (6348 elements) to ensure  ... 
doi:10.1080/10255842.2012.719606 pmid:22978574 pmcid:PMC3527685 fatcat:z2tp24gy4bderhtae3jvmi2gdi

Geometric morphometrics: recent applications to the study of evolution and development

A. M. Lawing, P. D. Polly
2010 Journal of Zoology  
measurement of developmental stability, the role of development in shaping evolution, and the special problem of measuring the shape of fossil specimens that are deformed from their original shape.  ...  The field of morphometrics is developing quickly and recent advances allow for geometric techniques to be applied easily to many zoological problems.  ...  Shape modelling with landmarks is also a useful tool to study the effects of deformation or modification on morphologic structure.  ... 
doi:10.1111/j.1469-7998.2009.00620.x fatcat:hhypvlwbfrevjlb6b5d737gemm

Analysis of displacements in beam structures and shells with middle developable surfaces

Marina Rynkovskaya, H.F. Abdul Amir, P.S. Khiew
2017 MATEC Web of Conferences  
The comparison of results got by methods of structural mechanics and shell theory for the shells with developable middle surfaces is given.  ...  Generally the displacements of the beams are calculated by the traditional methods of structural mechanics with the help of approximate formulas which provide good results for linear tasks.  ...  In a paper [7] , Elenitsky E.Ya. suggested the algorithm of static calculation of geometrically nonlinear compound thin structures with the help of linear differential equations of moment theory and considered  ... 
doi:10.1051/matecconf/201710816001 fatcat:yiygiw5yfzdjndbewfhv7h2dyi

Learning Part-Based Models for Animation from Surface Motion Capture

Margara Tejera, Adrian Hilton
2013 2013 International Conference on 3D Vision  
Surface motion capture (SurfCap) enables 3D reconstruction of human performance with detailed cloth and hair deformation.  ...  This extends the range of animation with natural surface deformation beyond the wholebody poses present in the SurfCap data. We illustrate successful use of our tool on three different characters.  ...  A critical step for editing captured mesh sequences is the temporal alignment to obtain a mesh structure with surface correspondence over time referred to as surface motion capture (SurfCap) [2] .  ... 
doi:10.1109/3dv.2013.29 dblp:conf/3dim/TejeraH13 fatcat:5vq25xpsc5awtldao6t4x7qdiy

Structures of Three-Manifilds [article]

Shing-Tung Yau
2006 arXiv   pre-print
In this talk, I survey on Poincare and geometrization conjecture.  ...  Geometric Analysis On the other hand, starting in the seventies, a group of geometers applied nonlinear partial differential equations to build geometric structures over a space.  ...  The number of parameters of conformal structures over a surface with genus g is 6g − 6.  ... 
arXiv:math/0607821v2 fatcat:32j2sfcm2rf6fpjhv2uwef3aau
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