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Laplace operator on functions (as a positive operator convention) canis defined by $\Delta=d^*d$ where $d:C^\infty(M)\to C^\infty(T^*M)$ is the exterior derivative.
Laplace operator on functions (as a positive operator convention) can defined by $\Delta=d^*d$ where $d:C^\infty(M)\to C^\infty(T^*M)$ is the exterior derivative.
Laplace operator on functions (as a positive operator convention) is defined by $\Delta=d^*d$ where $d:C^\infty(M)\to C^\infty(T^*M)$ is the exterior derivative.
Laplace operator on functions (as a positive operator convention) can defined by $\Delta=d^*d$ where $d:C^\infty(M)\to C^\infty(T^*M)$ is the exterior derivative.
