##### Department of Mathematics,

University of California San Diego

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### Differential Geometry

## Lei Ni

#### UCSD

## Poincare-Lelong equation via Hodge-Laplace heat equation

##### Abstract:

I shall explain how a new approach via the Hodge-Laplace heat equation works in solving the Poincare-Lelong equation. This method essentially is reduced to a uniqueness theorem and some estimates concluding the preservation of the d-closedeness of the solution of the Hodge-Laplace heat equation, and circumvents the essential difficulties of the elliptic method previously adapted by many people without being able to prove the best possible result. This is a joint work with Luen-Fai Tam.

Host: Paul Bryan

### January 17, 2013

### 9:00 AM

### AP&M 7218

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