We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate ...for the Spinc Dirac operator. This allows us to obtain eigenvalue estimates for the twisted Dirac operator appearing in the context of Dirac-harmonic maps and their extensions, from which we also obtain several Liouville type results.
Given a continuous complex-valued function
and nonnegative functions
and
on a two-dimensional smooth connected closed surface such that
and the functions
and
have no common zeros, it is required to ...find complex-valued continuous functions
and
satisfying the conditions
and
. Necessary and sufficient solvability conditions for this problem are given.
We give two new proofs of the well-known result that the moduli space
M
5
of equilateral plane pentagons is a closed surface of genus four. Moreover, we construct a new algebraic description of this ...space, also in the non-equilateral case, as a real affine algebraic surface
F
defined by a polynomial
p
(
x
,
y
,
z
) of degree 12. This allows a visualization using the Surfer software.
The present paper deals with the volume preserving smoothing of triangular isotropic meshes over three-dimensional surfaces. The adopted approach is based on Laplacian smoothing combining in an ...alternating manner positive and negative weights in consecutive cycles of the smoothing. Since the aim is to improve the shape of individual elements of the mesh rather than to get rid of a noise, the weights are derived in a very simple way using a “do not harm” concept. The paper also extends the smoothing methodology from meshes on closed surfaces to meshes on open surfaces and discusses how the concept can be applied to meshes over surfaces with sharp features and curvature discontinuities. The performance and capabilities of the presented smoothing approach are demonstrated on several examples.
The objective of the present work is to present information on the set of periodic points of a continuous self-map on a closed surface which can be obtained using the action of this map on ...homological groups of the closed surface.
We show that, for any given non-spherical orientable closed surface
F
2
, there exists an optimal 1-planar graph which can be embedded on
F
2
as a triangulation. On the other hand, we prove that ...there does not exist any such graph for the nonorientable closed surfaces of genus at most 3.
This study investigates surface waves propagating across a partially closed surface-breaking crack in concrete. The experimental program includes three concrete specimens and three test phases. In ...the first and second test phases, effects of compression and bending on the transmission ratio and phase velocity of surface waves were investigated in crack-free specimens. In the third phase, the surface wave parameters were measured on the specimens with a surface-breaking crack when a compressive load was applied to partially close the crack. Experimental results showed that both the wave transmission and velocity are sensitive to the compressive load when the crack is gradually closed. Variations of the surface wave parameters are presented with the compressive and tensile loads, and crack mouth opening displacement. Findings in this study will provide useful information for studying stress wave propagation across a partially closed crack and for applying the surface wave based nondestructive testing methods to actual concrete structures.
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Civita connection. In this article, we prove that an ...analogue of the uniformization theorem also holds for connections with metric torsion in the case of non-positive Euler characteristic. Our main tool is an adapted form of the Ricci flow.
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