scholarly journals The Wulff shape minimizes an anisotropic Willmore functional

2004 ◽  
pp. 351-359 ◽  
Author(s):  
Ulrich Clarenz
Keyword(s):  
Wulff Shape ◽  
Willmore Functional

On Uniqueness of the Wulff Shape for Cellular Automata

1991 ◽  
Vol 14 (1) ◽  
pp. 75-89
Author(s):  
Paweł Wlaź
Keyword(s):  
Cellular Automata ◽  
Large Class ◽  
Growth Function ◽  
Wulff Shape ◽  
Transition Rules

In this paper, ordered transition rules are investigated. Such rules describe an increment of mono-crystals and for every rule one can calculate so called Wulff Shape. It is shown that for some large class of these rules, there exists at most one growth function which generates a given Wulff Shape.

scholarly journals The Wulff shape as the asymptotic limit of a growing crystalline interface

1997 ◽  
Vol 1 (3) ◽  
pp. 560-571 ◽  
Author(s):  
Stanley Osher ◽  
Barry Merriman
Keyword(s):  
Asymptotic Limit ◽  
Wulff Shape

scholarly journals Wulff shape of strontium titanate nanocuboids

2015 ◽  
Vol 632 ◽  
pp. L22-L25 ◽  
Author(s):  
Lawrence Crosby ◽  
James Enterkin ◽  
Federico Rabuffetti ◽  
Kenneth Poeppelmeier ◽  
Laurence Marks
Keyword(s):  
Strontium Titanate ◽  
Wulff Shape

Local minimizers of the Willmore functional

Analysis ◽  
2015 ◽  
Vol 35 (2) ◽  
Author(s):  
Florian Skorzinski
Keyword(s):  
Critical Point ◽  
Local Minimizer ◽  
Positive Definite ◽  
Second Derivative ◽  
Sufficient Condition ◽  
Conformal Transformations ◽  
Willmore Functional ◽  
Local Minimizers

AbstractSince the Willmore functional is invariant with respect to conformal transformations and reparametrizations, the kernel of the second derivative of the functional at a critical point will always contain a subspace generated by these transformations. We prove that the second derivative being positive definite outside this space is a sufficient condition for a critical point to be a local minimizer.

scholarly journals Quasicrystals and the Wulff-Shape

1999 ◽  
Vol 21 (3) ◽  
pp. 421-436 ◽  
Author(s):  
K. Böröczky ◽  
U. Schnell
Keyword(s):  
Wulff Shape

scholarly journals Reflection of Willmore Surfaces with Free Boundaries

2020 ◽  
pp. 1-18
Author(s):  
Ernst Kuwert ◽  
Tobias Lamm
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Critical Points ◽  
Free Boundaries ◽  
Willmore Functional ◽  
Boundary Constraints ◽  
Free Boundary Conditions ◽  
Immersed Surfaces ◽  
Willmore Surfaces

Abstract We study immersed surfaces in ${\mathbb R}^3$ that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

scholarly journals STABILITY OF CRYSTALLINE EVOLUTIONS

2005 ◽  
Vol 15 (06) ◽  
pp. 921-937 ◽  
Author(s):  
MATTEO NOVAGA ◽  
EMANUELE PAOLINI
Keyword(s):  
Integral Curve ◽  
Jacobian Matrix ◽  
Convex Polyhedra ◽  
Wulff Shape ◽  
Stability Properties ◽  
Fixed Volume ◽  
The Stability

In this paper we analyze the stability properties of the Wulff-shape in the crystalline flow. It is well known that the Wulff-shape evolves self-similarly, and eventually shrinks to a point. We consider the flow restricted to the set of convex polyhedra, we show that the crystalline evolutions may be viewed, after a proper rescaling, as an integral curve in the space of polyhedra with fixed volume, and we compute the Jacobian matrix of this field. If the eigenvalues of such a matrix have real part different from zero, we can determine if the Wulff-shape is stable or unstable, i.e. if all the evolutions starting close enough to the Wulff-shape converge or not, after rescaling, to the Wulff-shape itself.

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