Uploading to Blobstore gives a Java heap OutOfMemoryError

I'm doing a very simple upload form to my Google App Engine application. In the client GWT code I have something like:

final FormPanel uploadForm = new FormPanel();
uploadForm.setEncoding(FormPanel.ENCODING_MULTIPART);
uploadForm.setMethod(FormPanel.METHOD_POST);

uploadBtn.addClickHandler(new ClickHandler() {
        @Override
        public void onClick(ClickEvent event) {
            blobstoreUploadURLService.getBlobstoreUploadURL("/banzai/process-pdf", new AsyncCallback<String>() {

                @Override
                public void onFailure(Throwable caught) {
                    // TODO Auto-generated method stub
                    System.err.println("FAILURE DURING UPLOAD SERVICE");
                }

                @Override
                public void onSuccess(String result) {
                    uploadForm.setAction(result);
                    uploadForm.submit();
                }

            });
        }
    });

And it uses a new FileUpload() to select the file. When I test it, either locally or on a deployed instance, I get the following error in the logs:

WARNING: Error for /_ah/upload/agdrYnNrYWFychsLEhVfX0Jsb2JVcGxvYWRTZXNzaW9uX18YAww java.lang.OutOfMemoryError: Java heap space
  at java.util.Arrays.copyOf(Arrays.java:2786)
  at java.io.ByteArrayOutputStream.write(ByteArrayOutputStream.java:71)
  at javax.mail.internet.MimeMultipart.readTillFirstBoundary(MimeMultipart.java:316)
  at javax.mail.internet.MimeMultipart.parse(MimeMultipart.java:186)
  at javax.mail.internet.MimeMultipart.getCount(MimeMultipart.java:109)
  at com.google.appengine.api.blobstore.dev.UploadBlobServlet.handleUpload(UploadBlobServlet.java:135)
  at com.google.appengine.api.blobstore.dev.UploadBlobServlet.access$000(UploadBlobServlet.java:72)
  at com.google.appengine.api.blobstore.dev.UploadBlobServlet$1.run(UploadBlobServlet.java:100)
  at java.security.AccessController.doPrivileged(Native Metho