| EPSRC Reference: |
GR/L57159/01 |
| Title: |
HEAT KERNEL ESTIMATES ON RIEMANNIAN MANIFOLDS |
| Principal Investigator: |
Grigor'Yan, Professor A |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
03 November 1997 |
Ends: |
02 November 1999 |
Value (£): |
6,000
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The main aim of the project is to create a consistent theory of lower bounds of the heat kernels on non-compact complete Riemannian manifolds. It is known that upper bounds of the heat kernel of Gaussian type are equivalent to certain isoperimetric properties of the manifolds and, thus, have a clear geometric explanation. For lower bounds, we have found that a on-diagonal estimate of the heat kernel can be stated in terms of the volume function. The question of finding geometric dependencies for heat kernel lower bounds of Gaussian type, has already been open for a long time. Our previous joint work has created a necessary background to attack this question.At the same time, we will touch adjacent question of sharper on-diagonal lower bound which should take into account certain subtle properties of the manifold. One of the aims of this part would be to geometrically explain a lower bound of the form exp(-t1/3) which appears for purely algebraic reasons.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.imperial.ac.uk |