According to the problem that how to increase the fidelity of simplified model, this paper put forward a method which using vertex clustering based on principal curvature. Our measure taking the gradual simplify thinking and simplifying the mesh model successive by quadric error metric and principal curvature based on integral invariants. We improve the defect of error accumulation which consis...

In this paper, we obtain the isoperimetric inequality on a conformally flat manifold with finite total Q-curvature. This is a higher dimensional analog of Li and Tam’s result [“Complete surfaces with finite total curvature.” Journal of Differential Geometry 33 (1991): 139–68] on surfaces with finite total Gaussian curvature. The main step in the proof is based on the construction of a quasiconf...

The collective migration of cells is fundamental to epithelial biology. One of the hallmarks of collective behavior in migrating cohesive epithelial cell sheets is the emergence of so called leader cells. These cells exhibit a distinct morphology with a large and highly active lamellipodium. Although it is generally accepted that they play a crucial part in collective migration, the biophysical...

Let G be an infinite graph embedded in a closed 2-manifold, such that each open face of the embedding is homeomorphic to an open disk and is bounded by finite number of edges. For each vertex x of G, define the combinatorial curvature KG(x) = 1− d(x) 2 + ∑ σ∈F (x) 1 |σ| as that of [9], where d(x) is the degree of x, F (x) is the multiset of all open faces σ in the embedding such that the closur...

I discuss an old result of John Milnor stating roughly that if a closed curve in space is not too curved then it cannot be knotted. CONTENTS 1. The total curvature of a polygonal curve 1 2. A probabilistic interpretation of the total curvature 2 3. The total curvature of a smooth closed curve 4 4. Total curvature and knotting 6 References 7 1. THE TOTAL CURVATURE OF A POLYGONAL CURVE An (orient...