Let M be a compct submanifold of sphere SN, and M be Cliford torus imbedding in SN. If Spec0(M) =Spec0(M), and Specq(M) =Specq(M), then author can obtaid that M is isometric to M.
Let M be a compact minimal hypersurface of sphere Sn+1(1). Let M be H(r)-torus of sphere Sn+1(1).Assume they have the same constant mean curvature H, the result in [1] is that if Spec0 (M, g) =Spec0(M, g),then for 3 ...Let M be a compact minimal hypersurface of sphere Sn+1(1). Let M be H(r)-torus of sphere Sn+1(1).Assume they have the same constant mean curvature H, the result in [1] is that if Spec0 (M, g) =Spec0(M, g),then for 3 ≤ n ≤ 6,r2 ≤n-1/n or n > 6,r2 ≥ n-1/n, then M is isometric to M. We improvedthe result and prove that: if Spec0(M, g) =Spec0(M, g), then M is isometric to M. Generally, if Specp(M,g) =Specp(M, g), here p is fixed and satisfies that n(n - 1) ≠ 6p(n - p), then M is isometric to M.展开更多
Let M be a closed extremal hypersurface in S^n＋1 with the same mean curvature of the Willmore torus Wm,n-m.We proved that if Spec^p（M） = Spec^p（Wm,n-m ） for p = 0, 1, 2, then M is Wm,m.
Non-rigid shape deformation without tearing or stretching is called isometry. There are many difficulties to research non-rigid shape in Euclidean space. Therefore, non-rigid shapes are firstly embedded into a none-Eu...Non-rigid shape deformation without tearing or stretching is called isometry. There are many difficulties to research non-rigid shape in Euclidean space. Therefore, non-rigid shapes are firstly embedded into a none-Euclidean space. Spectral space is chosen in this paper. Then three descriptors are proposed based on three spectral distances. The existence of zero-eigenvalue has negative effects on computation of spectral distance, Therefore the spectral distance should be computed from the first non-zcro-eigenvalue. Experiments show that spectral distance distributions are very effective to describe the non-rigid shapes.展开更多
Isometric 3D shape partial matching has attracted a great amount of interest, with a plethora of applicationsranging from shape recognition to texture mapping. In this paper, we propose a novel isometric 3D shape part...Isometric 3D shape partial matching has attracted a great amount of interest, with a plethora of applicationsranging from shape recognition to texture mapping. In this paper, we propose a novel isometric 3D shape partial matchingalgorithm using the geodesic disk Laplace spectrum （GD-DNA）. It transforms the partial matching problem into the geodesicdisk matching problem. Firstly, the largest enclosed geodesic disk extracted from the partial shape is matched with geodesicdisks from the full shape by the Laplace spectrum of the geodesic disk. Secondly, Generalized Multi-Dimensional Scalingalgorithm （GMDS） and Euclidean embedding are conducted to establish final point correspondences between the partialand the full shape using the matched geodesic disk pair. The proposed GD-DNA is discriminative for matching geodesicdisks, and it can well solve the anchor point selection problem in challenging partial shape matching tasks. Experimentalresults on the Shape Retrieval Contest 2016 （SHREC＇16） benchmark validate the proposed method, and comparisons withisometric partial matching algorithms in the literature show that our method has a higher precision.展开更多
文摘Let M be a compct submanifold of sphere SN, and M be Cliford torus imbedding in SN. If Spec0(M) =Spec0(M), and Specq(M) =Specq(M), then author can obtaid that M is isometric to M.
基金Supported by National Natural Science Foundation of China (10371047)
文摘Let M be a compact minimal hypersurface of sphere Sn+1(1). Let M be H(r)-torus of sphere Sn+1(1).Assume they have the same constant mean curvature H, the result in [1] is that if Spec0 (M, g) =Spec0(M, g),then for 3 ≤ n ≤ 6,r2 ≤n-1/n or n > 6,r2 ≥ n-1/n, then M is isometric to M. We improvedthe result and prove that: if Spec0(M, g) =Spec0(M, g), then M is isometric to M. Generally, if Specp(M,g) =Specp(M, g), here p is fixed and satisfies that n(n - 1) ≠ 6p(n - p), then M is isometric to M.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper it is proved that the essential spectrum ot some class of Riemannian mani-folds with nonnegative radical sectional curvature is [0, +∞).
文摘Let M be a closed extremal hypersurface in S^n＋1 with the same mean curvature of the Willmore torus Wm,n-m.We proved that if Spec^p（M） = Spec^p（Wm,n-m ） for p = 0, 1, 2, then M is Wm,m.
基金Partly Supported by NKBRPC(2004CB318006)NNSFC(60873164 and 60533090)
文摘Non-rigid shape deformation without tearing or stretching is called isometry. There are many difficulties to research non-rigid shape in Euclidean space. Therefore, non-rigid shapes are firstly embedded into a none-Euclidean space. Spectral space is chosen in this paper. Then three descriptors are proposed based on three spectral distances. The existence of zero-eigenvalue has negative effects on computation of spectral distance, Therefore the spectral distance should be computed from the first non-zcro-eigenvalue. Experiments show that spectral distance distributions are very effective to describe the non-rigid shapes.
基金This work was supported by the National Key Technology Research and Development Program of China under Grant No. 2017YFB1002804, and the National Natural Science Foundation of China under Grant Nos. 61672103, 61731015, 61572078 and 61402042.
文摘Isometric 3D shape partial matching has attracted a great amount of interest, with a plethora of applicationsranging from shape recognition to texture mapping. In this paper, we propose a novel isometric 3D shape partial matchingalgorithm using the geodesic disk Laplace spectrum （GD-DNA）. It transforms the partial matching problem into the geodesicdisk matching problem. Firstly, the largest enclosed geodesic disk extracted from the partial shape is matched with geodesicdisks from the full shape by the Laplace spectrum of the geodesic disk. Secondly, Generalized Multi-Dimensional Scalingalgorithm （GMDS） and Euclidean embedding are conducted to establish final point correspondences between the partialand the full shape using the matched geodesic disk pair. The proposed GD-DNA is discriminative for matching geodesicdisks, and it can well solve the anchor point selection problem in challenging partial shape matching tasks. Experimentalresults on the Shape Retrieval Contest 2016 （SHREC＇16） benchmark validate the proposed method, and comparisons withisometric partial matching algorithms in the literature show that our method has a higher precision.
