Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Analysis of PDEs

arXiv:1405.6373 (math)
[Submitted on 25 May 2014 (v1), last revised 19 Apr 2024 (this version, v5)]

Title:On space-time quasiconcave solutions of the heat equation

Authors:Chuanqiang Chen, Xi-Nan Ma, Paolo Salani
View PDF
Abstract:In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas and for completeness, we also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1405.6373 [math.AP]
  (or arXiv:1405.6373v5 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1405.6373

Submission history

From: Chuanqiang Chen [view email]
[v1] Sun, 25 May 2014 10:37:25 UTC (37 KB)
[v2] Mon, 1 Feb 2016 01:08:18 UTC (46 KB)
[v3] Fri, 25 May 2018 23:39:37 UTC (1 KB) (withdrawn)
[v4] Mon, 11 Mar 2019 14:32:05 UTC (44 KB)
[v5] Fri, 19 Apr 2024 11:50:14 UTC (44 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.AP
< prev   |   next >
new | recent | 2014-05
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)