Self?repulsiveness of energies for closed submanifolds
نویسندگان
چکیده
We show that the regularized Riesz $\a$-energy for closed submanifolds $M$ in $\RR^n$ blows up as degenerates to have double points if $\a\le-2\dim M$. This gives theoretical foundation of numerical experiments evolve surfaces decrease energy which been carried out since 90's.
منابع مشابه
Total Diameter and Area of Closed Submanifolds
The total diameter of a closed planar curve C ⊂ R is the integral of its antipodal chord lengths. We show that this quantity is bounded below by twice the area of C. Furthermore, when C is convex or centrally symmetric, the lower bound is twice as large. Both inequalities are sharp and the equality holds in the convex case only when C is a circle. We also generalize these results to m dimension...
متن کاملStable closed equilibria for anisotropic surface energies: Surfaces with edges
We study the stability of closed, not necessarily smooth, equilibrium surfaces of an anisotropic surface energy for which the Wulff shape is not necessarily smooth. We show that if the Cahn Hoffman field can be extended continuously to the whole surface and if the surface is stable, then the surface is, up to rescaling, the Wulff shape. 2010 AMS classification: 49Q10
متن کاملSignature submanifolds for some equivalence problems
This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.
متن کاملRicci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
متن کاملVanishing theorems for associative submanifolds
Let M7 a manifold with holonomy in G2, and Y 3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that MX,Y , the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner’s technique, we give a vanishing theorem that forces MX,Y to be locally smooth. MSC 2000: 53C38 (35J55, 53C21, 58J32).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2022
ISSN: ['1522-2616', '0025-584X']
DOI: https://doi.org/10.1002/mana.202000158