Matches in SemOpenAlex for { <https://semopenalex.org/work/W4301476280> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W4301476280 abstract "We study the motion of smooth, closed, strictly convex hypersurfaces in $mathbb{R}^{n+1}$ expanding in the direction of their normal vector field with speed depending on the $k$th elementary symmetric polynomial of the principal radii of curvature $sigma_k$ and support function $h$. A homothetic self-similar solution to the flow that we will consider in this paper, if exists, is a solution of the well-known $L_p$-Christoffel-Minkowski problem $varphi h^{1-p}sigma_k=c$. Here $varphi$ is a preassigned positive smooth function defined on the unit sphere, and $c$ is a positive constant. For $1leq kleq n-1, pgeq k+1$, assuming the spherical hessian of $varphi^{frac{1}{p+k-1}}$ is positive definite, we prove the $C^{infty}$ convergence of the normalized flow to a homothetic self-similar solution. One of the highlights of our arguments is that we do not need the constant rank theorem/deformation lemma of Guan-Ma and thus we give a partial answer to a question raised in Guan-Xia. Moreover, for $k=n, pgeq n+1$, we prove the $C^{infty}$ convergence of the normalized flow to a homothetic self-similar solution without imposing any further condition on $varphi.$ In the final section of the paper, for $1leq k<n$, we will give an example that spherical hessian of $varphi^{frac{1}{p+k-1}}$ is negative definite at some point and the solution to the flow loses its smoothness." @default.
- W4301476280 created "2022-10-05" @default.
- W4301476280 creator A5019920891 @default.
- W4301476280 date "2018-03-22" @default.
- W4301476280 modified "2023-09-23" @default.
- W4301476280 title "Deforming a hypersurface by principal radii of curvature and support function" @default.
- W4301476280 doi "https://doi.org/10.48550/arxiv.1803.08470" @default.
- W4301476280 hasPublicationYear "2018" @default.
- W4301476280 type Work @default.
- W4301476280 citedByCount "0" @default.
- W4301476280 crossrefType "posted-content" @default.
- W4301476280 hasAuthorship W4301476280A5019920891 @default.
- W4301476280 hasBestOaLocation W43014762801 @default.
- W4301476280 hasConcept C114410712 @default.
- W4301476280 hasConcept C114614502 @default.
- W4301476280 hasConcept C134306372 @default.
- W4301476280 hasConcept C164226766 @default.
- W4301476280 hasConcept C16977076 @default.
- W4301476280 hasConcept C175017881 @default.
- W4301476280 hasConcept C191948623 @default.
- W4301476280 hasConcept C195065555 @default.
- W4301476280 hasConcept C199360897 @default.
- W4301476280 hasConcept C2524010 @default.
- W4301476280 hasConcept C2777027219 @default.
- W4301476280 hasConcept C33923547 @default.
- W4301476280 hasConcept C41008148 @default.
- W4301476280 hasConcept C91709909 @default.
- W4301476280 hasConceptScore W4301476280C114410712 @default.
- W4301476280 hasConceptScore W4301476280C114614502 @default.
- W4301476280 hasConceptScore W4301476280C134306372 @default.
- W4301476280 hasConceptScore W4301476280C164226766 @default.
- W4301476280 hasConceptScore W4301476280C16977076 @default.
- W4301476280 hasConceptScore W4301476280C175017881 @default.
- W4301476280 hasConceptScore W4301476280C191948623 @default.
- W4301476280 hasConceptScore W4301476280C195065555 @default.
- W4301476280 hasConceptScore W4301476280C199360897 @default.
- W4301476280 hasConceptScore W4301476280C2524010 @default.
- W4301476280 hasConceptScore W4301476280C2777027219 @default.
- W4301476280 hasConceptScore W4301476280C33923547 @default.
- W4301476280 hasConceptScore W4301476280C41008148 @default.
- W4301476280 hasConceptScore W4301476280C91709909 @default.
- W4301476280 hasLocation W43014762801 @default.
- W4301476280 hasOpenAccess W4301476280 @default.
- W4301476280 hasPrimaryLocation W43014762801 @default.
- W4301476280 hasRelatedWork W2014322176 @default.
- W4301476280 hasRelatedWork W2040887405 @default.
- W4301476280 hasRelatedWork W2046982427 @default.
- W4301476280 hasRelatedWork W2361290932 @default.
- W4301476280 hasRelatedWork W2363969488 @default.
- W4301476280 hasRelatedWork W2735213556 @default.
- W4301476280 hasRelatedWork W2791427667 @default.
- W4301476280 hasRelatedWork W2950551340 @default.
- W4301476280 hasRelatedWork W2991179030 @default.
- W4301476280 hasRelatedWork W4301476280 @default.
- W4301476280 isParatext "false" @default.
- W4301476280 isRetracted "false" @default.
- W4301476280 workType "article" @default.